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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]
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]
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
[AIEEE2005]
Let A and B be two events such that complement of event A. Then events A and B are 
[AIEEE2005]
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} + 7^{n} 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 P_{1}, P_{2}, P_{3}, .............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 P_{4} 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.)]
There are n urns each containing n + 1 balls such that the i^{th} urn contains i whiteballs and (n + 1 – i) red balls. Let u_{i} be the event of selecting
i^{th} urn, i = 1, 2, 3..........n and W denotes the event of getting a white ball.
[JEE 2006, 5+5+5]
There are n urns each containing n + 1 balls such that the i^{th} urn contains i whiteballs and (n + 1 – i) red balls. Let u_{i} be the event of selecting
i^{th} urn, i = 1, 2, 3..........n and W denotes the event of getting a white ball.
If n is even and E denotes the event of choosing even numbered urn then the value of P(W / E), is
An experiment has 10 equally likely outcomes. Let A and B be two nonempty 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]
Consider the system of equations ax + by = 0, cx + dy = 0, where a, b, c, d ∈ {0, 1}
Statement1 : The probability that the system of equations has a unique solution is 3/8.
Statement2 : The probability that the system of equations has a solution is 1.
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
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]
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]
Paragraph for Question Nos. 16 to 17
Let U_{1} and U_{2} be two urns such that U_{1} contains 3 white and 2 red balls, and U_{2} contains only 1 white ball.A fair coin is tossed. If head appears then 1 ball is drawn at random from U_{1} and put into U_{2}. However, if tail appears then 2 balls are drawn at random from U_{1} and put into U_{2}. Now 1 ball is drawn at random from U_{2}.
The probability of the drawn ball from U_{2} being white is
[JEE 2011]
Let U_{1} and U_{2} be two urns such that U_{1} contains 3 white and 2 red balls, and U_{2} contains only 1 white ball.A fair coin is tossed. If head appears then 1 ball is drawn at random from U_{1} and put into U_{2}. However, if tail appears then 2 balls are drawn at random from U_{1} and put into U_{2}. Now 1 ball is drawn at random from U_{2}.
Given that the drawn ball from U_{2} is white, the probability that head appeared on the coin is
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]
A ship is fitted with three engines E_{1}, E_{2} and E_{3}. 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 X_{1}, X_{2} and X_{3} denote respectively the events that the engines E_{1} , E_{2} and E_{3} are functioning. Which of the following is (are) true ?
[JEE 2012]
Fou r fai r dice D_{1}, D_{2}, D_{3} and D_{4}, each h avi ng si x faces numbered 1, 2 , 3, 4, 5 and 6, ar e rolled simultaneously. The probability that D_{4} shows a number appearing on one of D_{1}, D_{2} and D_{3} is
[JEE 2012]
Let X and Y be two events such that Which of the following is (are) correct ?
[JEE 2012]
204 videos288 docs139 tests

Variance of Random Variable  Probability, Class 12, Math Video  06:44 min 
Binomial Distribution  Probability, Class 12, Math Video  10:03 min 
Mean of a Random Variable  Probability, Class 12, Math Video  03:16 min 
What are Bernoulli Trials?  Probability, Class 12, Math Video  04:30 min 
Bayes' Theorem  Probability, Class 12, Math Video  12:30 min 
204 videos288 docs139 tests

Variance of Random Variable  Probability, Class 12, Math Video  06:44 min 
Binomial Distribution  Probability, Class 12, Math Video  10:03 min 
Mean of a Random Variable  Probability, Class 12, Math Video  03:16 min 
What are Bernoulli Trials?  Probability, Class 12, Math Video  04:30 min 
Bayes' Theorem  Probability, Class 12, Math Video  12:30 min 