Test: JEE Previous Year Questions- Probability - JEE MCQ

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

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]

Probability of occurrence of an event lies between

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]

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

[AIEEE 2004]

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]

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

[AIEEE-2005]

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

[AIEEE 2007]

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]

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]

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

[AIEEE 2008]

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]

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]

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]

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]

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]

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]

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]

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]

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

[JEE 99]

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 ?

Eight players P₁, P₂, P₃, .............P8 play a knockout tournament. It is known that whenever the players P_i and P_j play, the player P_i 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

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

[REE 99, 6]

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)]

 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.

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]

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

 [JEE 2005 (Scr.)]