Probability Assignment - JEE2021

Q1. Words are formed with the letters of the word PEACE. Find the probability that 2 E’s come together.

A

B

D

C

None of these

Q2. If four cards are drawn at random from a pack of fifty-two playing cards, find the probability that at least one of them is an ace.

A

B

D

C

0.24

0.72

0.64

0.28

Q3. Three coins are tossed. If one of them shows tail, then find the probability that all three coins show tail.

A

B

D

C

None of these

Q4. A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is

A

B

D

C

None of these

Q5. It is given that the events A and B are such that

A

B

D

C

Q6. The probability that a certain kind of component will survive a

given shock test . Find the probability that among 5 components

tested exactly 2 will survive.

A

B

D

C

None of these

Q7. A pair of dice is thrown. If the sum of numbers that turned up on the two dice is 8, then the probability that the number turn upon the second die is 5 is?

A

B

D

C

Q8. A certain team wins with probability 0.7, loses with probability 0.2 and ties with probability 0.1. The team plays three games. What is the probability that team wins at least2 games but not lose?

A

B

0.14

0.35

D

C

0.69

0.49

Q9. If a random variable X takes value 0 and 1 with respective

probabilities then the expected value of X is

A

B

D

C

1

0

Q10. A die is thrown 7 times. What is the chance that an odd number turns up at least 4 times?

A

B

D

C

Q11. If A and B are independent events with P(A) = 0.3 and P(B) = 0.4, then find the value of P(A ∪ B).

A

B

D

C

0.8

0.3

0.7

0.4

Q12. A box contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is . The number of blue balls in the jar is:

A

B

D

C

8

13

12

16

Q13. Box I contains 30 cards numbered 1 to 30 and box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:

A

B

D

C

02-09-2020 - Morning Shift

Q14. There are 20 marbles in a bag and 10 of them are blue. What is the probability that any 1 marble drawn at random will not be blue?

A

B

D

C

Q15. then find P(A ∩ B), if A and B are

independent events.

A

B

D

C

Q16. A fair coin is tossed 100 times and the head occurs 58 times and tail 42 times. The experimental probability of getting a head is:

A

B

D

C

Q17. A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, then find the probability that the other is also good.

A

B

D

C

None of these

Q18. What is the probability of guessing correctly at least 8 out of 10

answers on a true-false examination?

A

B

D

C

Q19. Find the probability of getting at least one tail in 4 tosses of a coin.

A

B

D

C

None of these

Q20. then find the value of

A

B

D

C

Q21. The probability that a randomly chosen 5 - digit number is made from exactly two digits is:

A

B

D

C

03-09-2020 - Evening Shift

Q22. If , then the odds against the event A is

A

B

D

C

5 : 14

5 : 9

5 : 4

4 : 5

Q23. In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then find the probability that he was guessing.

A

B

D

C

None of these

Q24. Let A, B, C, D be independent events such that

. Then the probability that none of A, B, C and D occurs

A

B

D

C

None of these

Q25. If X follows a binomial distribution with parameters n = 100 and , then P(x = r) is maximum when r =

A

B

D

C

None of these

33

50

25

Q26. The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is:

08-04-2019 - Evening Shift

Integer Type

Q27. If the probability that the product of the outcomes of three rolls

of a fair dice is a prime number is p, then the value of is.

Integer Type

Q28. If the probability of a six-digit number N whose six digits are 1, 2,

3, 4, 5, 6 written as random order is divisible by 6 is p then the value of

is.

Integer Type

Q29. The probability of a man hitting a target is . The least number

of shots required, so that the probability of his hitting the target at

least once is greater than , is…...

04-09-2020 - Morning Shift

Integer Type

Q30. If A and B are two events such that P(A) = 0.6 P(B) = 0.8, if the

greatest value that can have is p, then the value of 8p is.

Integer Type

Q31. If A and B are two independent events such that

then

A

B

D

C

Multiple Correct Type

A

B

D

C

P(A) = 0.3

P(A ⋃ B) = 0.55

Q32. Let A and B be two events such that P(A ⋂ B’)=0.20, P(A’⋂ B) = 0.15 and P(A and B both fail) = 0.10. Then

Multiple Correct Type

A

B

D

C

None of these

The probability that married couple watches the show is 0.35

The probability that a wife watches the show given that her husband does is 7/8The probability that at least one person of a married couple will watch the show is 0.55

Q33. The probability that a married man watches a certain TV show is 0.4 and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Then

Multiple Correct Type

Q34. If A and B are two events, the probability that exactly one of them occurs is given by

A

B

D

C

P(A) + P(B) - 2P(A ∩ B)

P(A ⋃ B) - P(A ∩ B)

Multiple Correct Type

Q35. A fair coin is tossed 99 times. Let X be the number of times heads occurs. Then P(X=r) is maximum when r is

A

B

D

C

50

49

52

51

Multiple Correct Type

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