Test: JEE Previous Year Questions- Probability - JEE MCQ

# Test: JEE Previous Year Questions- Probability - JEE MCQ

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## 44 Questions MCQ Test Mathematics (Maths) Class 12 - Test: JEE Previous Year Questions- Probability

Test: JEE Previous Year Questions- Probability for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: JEE Previous Year Questions- Probability questions and answers have been prepared according to the JEE exam syllabus.The Test: JEE Previous Year Questions- Probability MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: JEE Previous Year Questions- Probability below.
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Test: JEE Previous Year Questions- Probability - Question 1

### If the probability of solving a problem by three students are 1/2, 2/3 and 1/4 then probability that the problem will be solved- [AIEEE 2002]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 1

Test: JEE Previous Year Questions- Probability - Question 2

### [AIEEE 2002]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 2

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Test: JEE Previous Year Questions- Probability - Question 3

### A pair of dice is thrown. If 5 appears on at least one of the dice, then the probability that the sum is 10 or greater, is -[AIEEE 2002]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 3

Let A be the event that 5 appears on at least one of dice let B be the event that sum is 10 or greater.

Test: JEE Previous Year Questions- Probability - Question 4

Events A, B, C are mutually exclusive events such that P(A)  The set of possible values of x are in the interval-

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 4

Test: JEE Previous Year Questions- Probability - Question 5

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is-

[AIEEE 2003]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 5

Let H1H2H3H4 B be the horses in which B is the winning horse.
Required probability

Test: JEE Previous Year Questions- Probability - Question 6

Probability of occurrence of an event lies between

Test: JEE Previous Year Questions- Probability - Question 7

A random variable X has the probabil ity distribution : For the events E = {X is a prime number} and F = {X < 4}, the probability P(E ∪ F) is

[AIEEE 2004]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 7

P (E) = P (2 or 3 or 5 or 7) = 0.23 + 0.12 + 0.20 + 0.07
= 0.6
P (F) = P (1 or 2 or 3)
= 0.15 + 0.23 + 0.12
= 0.50
P (E ⋂ F) = P (2 OR 3)=0.23+0.12=0.35
P (E ⋂ F) = P (E) + P (F) - P (E U F)
0.35 = 0.62 + 0.50 - P (E U F)
= 0.77

Test: JEE Previous Year Questions- Probability - Question 8

The mean and the variance of binominal distribution are 4 and 2 respectively.Then the probability of 2 successes is-

[AIEEE 2004]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 8

mean =4
np=4 and variance =2
npq=2
⇒4q=2
⇒q=1/2
∴p=1−q
= 1−1/2 = 1/2 also n=8 probability of 2 successes
p(x=2)=8C2p2q6
=[8!/(2!×6!)]×(1/2)2×(1/2)^6
=28×1/2(8)= 28/256

Test: JEE Previous Year Questions- Probability - Question 9

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

-[AIEEE-2005]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 9

Any person can apply for any house.
Required probability

Test: JEE Previous Year Questions- Probability - Question 10

Let A and B be two events such that    complement of event A. Then events A and B are -

[AIEEE-2005]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 10

Test: JEE Previous Year Questions- Probability - Question 11

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is-

[AIEEE 2007]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 11

Probability of getting a score of 9 twice is Required probability

Test: JEE Previous Year Questions- Probability - Question 12

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hi t correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is-

[AIEEE 2007]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 12

Required probability

Test: JEE Previous Year Questions- Probability - Question 13

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then  P (A ∪ B) is

[AIEEE 2008]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 13

Test: JEE Previous Year Questions- Probability - Question 14

It is given that the events A and B are such that

[AIEEE 2008]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 14

Test: JEE Previous Year Questions- Probability - Question 15

In a binomial distribution   f the probability of at least one success is greater than or equal to 9/10, then n is greater than :

[AIEEE 2009]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 15

Test: JEE Previous Year Questions- Probability - Question 16

One ticket is selected at random from 50 tickets numbered 00, 01, 02, ......., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals :

[AIEEE 2009]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 16

Let A be the event that sum of digits on selected ticket is 8 let B be the event that product is zero.

Test: JEE Previous Year Questions- Probability - Question 17

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

[AIEEE 2010]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 17

Required probability

Test: JEE Previous Year Questions- Probability - Question 18

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}.

Statement – 1: The probability that the chosen numbers when arranged in some order will form an AP is1/85.

Statement – 2: If the four chosen numbers form an AP, then the set of all possible values of common diference is {±1, ±2, ±3, ±4, ±5}

[AIEEE 2010]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 18

Test: JEE Previous Year Questions- Probability - Question 19

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32,then p lies in the interval :

[AIEEE 2011]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 19

Test: JEE Previous Year Questions- Probability - Question 20

If C and D ar e two even ts such th at C ⊂ D and P(D) ≠ 0, th en the cor rect statement among the following is :

[AIEEE 2011]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 20

Test: JEE Previous Year Questions- Probability - Question 21

Three numbers are chosen at random without replacement from {1, 2, 3, ....8}. The probability that their minimum is 3, given that their maximum is 6, is :

[AIEEE 2012]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 21

Let A be the event that minimum is 3 and let B be the event that their maximum is 6

Test: JEE Previous Year Questions- Probability - Question 22

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

[JEE -MAIN 2013]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 22

Test: JEE Previous Year Questions- Probability - Question 23

If the integers m and n are chosen at random from 1 and 100, then the probability that a number of the form 7m + 7n is divisible by 5 equals

[JEE 99]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 23

7m + 7n  divisible by 5
7n[7(m−n)+1]
7(m−n)+1 should be divisible by 5
Power of 7 has last digits revolving in 7,9,3,1.
7(m−n) should have last digit as 9.
7(m−n) = 7(4p+2)
m−n=4p+2
4p+2 ≤ 100
p ≤ 24.5
favorable=25,      total cases=100
P=25/100 = 1/4

Test: JEE Previous Year Questions- Probability - Question 24

The probability that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively.Of these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two, and a 40% chance of passing in exactly two, which of the following relations are true ?

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 24

Test: JEE Previous Year Questions- Probability - Question 25

Eight players P1, P2, P3, .............P8 play a knockout tournament. It is known that whenever the players Pi and Pj play, the player Pi will win if i < j. Assuming that the players are paired at random in each round, what is the probability that the players P4 reaches the final

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 25

Given that if Pi, Pj play with i < j, then Pi will win. For the first round, P4 should be paired with any one from P5 to P8. It can be done in 4C1  ways. Then P4 to be the finalist, at least one player from P5 to P8 should reach in the second round. Therefor, one pair should be from remaining 3 from P\ to P8 in 3C2 Then favourable pairing in first round is 4C1 3C2 3C2. Then in the 2nd round, we have four players.
Favourable ways in 1. Now total possible pairings is

*Answer can only contain numeric values
Test: JEE Previous Year Questions- Probability - Question 26

Four cards are drawn from a pack of 52 playing cards. Find the probability of drawing exactly one pair.

[REE 99, 6]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 26

There are 13 sets of the same card. We can choose 1 of the 13 in 13C1 = 13 ways. In that set, there are 4 cards. We can select 2 of the 4 in 4C2 =6 ways.The other 2 cards should not form a pair. Hence, we cannot select any card from the set we have selected the first 2 cards. Thus, there are 12 sets left. We need to select 2 sets from the 12 and after that 1 card out of 4 cards from each set. This can be done in 12C2 × 4C1 × 4C1 ways.
Hence, probability = (13 × 4C2 × 12C2 × 4C1 × 4C1)/52C4
= 6336/20825
=0.30

Test: JEE Previous Year Questions- Probability - Question 27

Two cards are drawn at random from a pack of playing cards. Find the probability that one card is a heart and the other is an ace.

[REE 2001 (Mains)]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 27

1/26 is the probability of getting a heart or an ace when drawing a single card from a deck of 52 cards.

Test: JEE Previous Year Questions- Probability - Question 28

In a combat, A targets B, and both B and C target A. The probabilities of A, B, C hitting their targets are 2/3, 1/2 and 1/3 respectively. They shoot simultaneously and A is hit. Find the probability that B hits his target whereas C does not.

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 28

P(A) = A hitting B = ⅔
P(B) = B hitting A = ½
P(C) = C hitting A = ⅓
P(E) = A is hit = P(BUC)
= 1 - P(B’⋂C’)
P(E) = 1 - P(B’)P(C’)
=> 1 - (1 - ½) (1 - ⅓)
=> ⅔
P(B⋂C’/E) = P(B⋂C’)/P(E)
= [P(B) P(C’)]/P(E)
=(½ * ⅔)/(⅔)
= 1/2

Test: JEE Previous Year Questions- Probability - Question 29

Three distinct numbers are selected from first hundred natural numbers. The probability that all the three numbers are divisible by 2 and 3 is

[JEE 2004]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 29

If a number is to be divisible by both 2 and 3, it should be divisible by their L.C.M., L.C.M of 2 and 3 is 6. The numbers are 6, 12, 18, ....., 96. The total number is 16.
Hence, the probability is :

Test: JEE Previous Year Questions- Probability - Question 30

A fair dice is thrown until 1 comes, then probability that 1 comes in even number of trials is

[JEE 2005 (Scr.)]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 30

In single throw of a dice, probability of getting 1 is 1/6 and probability of not getting 1 is 5/6.
Then, getting 1 in even number of changes is getting 1 in 2nd change or in 4th change or in 6thchange  and so on. Therefore, the required probability is

Test: JEE Previous Year Questions- Probability - Question 31

There are n urns each containing n + 1 balls such that the ith urn contains i whiteballs and (n + 1 – i) red balls. Let ui be the event of selecting

ith urn, i = 1, 2, 3..........n and W denotes the event of getting a white ball.

[JEE 2006, 5+5+5]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 31

Test: JEE Previous Year Questions- Probability - Question 32

There are n urns each containing n + 1 balls such that the ith urn contains i whiteballs and (n + 1 – i) red balls. Let ui be the event of selecting

ith urn, i = 1, 2, 3..........n and W denotes the event of getting a white ball.

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 32

Test: JEE Previous Year Questions- Probability - Question 33

If n is even and E denotes the event of choosing even numbered urn   then the value of P(W / E), is

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 33

Test: JEE Previous Year Questions- Probability - Question 34

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment.If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is

[JEE 2008]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 34

Let n(B)and n(A∩B)denote the number outcomes favourable to B and A∩B respectively.
As A and B are independent.
P(A∩B)=P(A)P(B)
⇒ n(A∩B)/10 = 4/10 × n(B)/10
⇒5n(A∩B)=2n(B)
⇒5∣n(B)
⇒nb=5 or 10. [∵1≤nb≤10.]

Test: JEE Previous Year Questions- Probability - Question 35

Consider the system of equations ax + by = 0, cx + dy = 0, where a, b, c, d ∈ {0, 1}

Statement-1 : The probability that the system of equations has a unique solution is 3/8.

Statement-2 : The probability that the system of equations has a solution is 1.

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 35

Favourable number fo caes is 6 (either ad = 1, bc =0 or ad = 0, bc =1). The probability that system of equation has unique solution is 6/16 = 3/8. Since x = 0 satisfies both the equations, the system has at least one solution.

Test: JEE Previous Year Questions- Probability - Question 36

A fair die is tossed repeatedly until a six is obtained. Let X denA fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. ]The probability that X = 3 equals

[JEE 2009

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 36

Test: JEE Previous Year Questions- Probability - Question 37

A fair die is tossed repeatedly until a six is obtained. Let X denA fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required. The probability that X > 3 equals

[JEE 2009]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 37

Test: JEE Previous Year Questions- Probability - Question 38

A signal which can be green or red with probability 4/5  and 1/5 respectively, is received by station A andthen transmitted to station B. The probability of each station receiving the signal correctly is 3/4, if the signal received at station B is green, then the probability that the original signal was green is

[JEE 2010]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 38

Event G = original signal is green

E1 = A recevies the signal correct

E2 = B recevies the signal correct

Test: JEE Previous Year Questions- Probability - Question 39

Paragraph for Question Nos. 16 to 17

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball.A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.

The probability of the drawn ball from U2 being white is

[JEE 2011]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 39

Test: JEE Previous Year Questions- Probability - Question 40

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball.A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now 1 ball is drawn at random from U2.

Given that the drawn ball from U2 is white, the probability that head appeared on the coin is

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 40

Test: JEE Previous Year Questions- Probability - Question 41

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25 .If P(T) denotes the probability of occurrence of the event T,, then

[JEE 2011]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 41

*Multiple options can be correct
Test: JEE Previous Year Questions- Probability - Question 42

A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective probabilities 1/2,1/4 and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the events that the engines E1 , E2 and E3 are functioning. Which of the following is (are) true ?

[JEE 2012]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 42

Test: JEE Previous Year Questions- Probability - Question 43

Fou r fai r dice D1, D2, D3 and D4, each h avi ng si x faces numbered 1, 2 , 3, 4, 5 and 6, ar e rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

[JEE 2012]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 43

Four fair dices rolled simultaneously.
Total number of outcomes=6×6×6×6
Suppose, the out come of the last one does not appear in the first three.
The number of such outcomes possible=6×(5)3
(∵D1 can show any of 6 numbers and first three can show any of the remaining 5 numbers)
Hence, probability that D4 does not show a number shown by any of D1,D2 or D3
​=[6×(5)3]/(6)4
So, the required probability =1−[6×(5)3]/(6)4
= 91/(216)

*Multiple options can be correct
Test: JEE Previous Year Questions- Probability - Question 44

Let X and Y be two events such that   Which of the following is (are) correct ?

[JEE 2012]

Detailed Solution for Test: JEE Previous Year Questions- Probability - Question 44

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## Mathematics (Maths) Class 12

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