Following are model questions on Mathematics (Probability) for the benefit of JEE Main Candidates. The questions may also useful for Advanced candidates. The key is also provided along with model questions.

1. Assertion (A): Two events A, B are independent ⇒ A, B are mutually exclusive

Reason (R): A, B are independent events ⇒ A ∩ B = φ

1) Both A, R are true and R is the correct explanation of A.

2) Both A, R are true and R is not the correct explanation of A.

3) A is true but R is false

4) A is false and R is false

2. A and B are two independent events of a sample space, such that P(A) = 0.2 and P(B) = 0.5

List – I List – II

A. P(B/A) 1. 0.2

B. P(A/B) 2. 0.1

C. P(A ∩ B) 3. 1

D. P(A ∪ B) 4 . 0.6

5. 0.5

The correct match for List I from List II is

A B C D

1) 4 5 3 1

3) 5 3 2 4

A B C D

2) 5 1 2 4

4) 5 1 3 4

3. Suppose Bag A has 6 white and 6 black balls and Bag B has 6 white and 5 black balls. Then, probability of getting 1 white ball, and 1 black ball I) When 2 balls are drawn from bag A is 6/11 II) When 2 balls are drawn from bag B is 6/11 Which is true

1) Only I 2) Only II

3)Both I and II 4) Neither I nor II

4. When 2 dice are thrown together

If A = Total score is 4

B = Total score is 8

C = Total score is 11, then ascending order

of P(A), P(B), P(C)

1) P(A) < P(B) < P(C) 2) P(C) < P(B) < P(A) 3) P(C) < P(A) < P(B) 4) P(A) < P(C) < P(B) 5. Five coins whose faces are marked 3, 4 are thrown. The chance of getting a total of 18 is 1) 1/32 2) 1/16 3) 3/16 4) 5/16 6. One number is selected at random from 1 to 900. The probability that it is a perfect square is 1) 1/10 2) 2/5 3) 3/10 4) 1/30 7. If two numbers are randomly selected from 20 consecutive natural numbers, then the probability that the sum of the two numbers is an odd number is 1) 9/19 2) 10/19 3) 142/145 4) 136/145 8. Three numbers are chosen from 1 to 30. The probability that they are not consecutive is 1) 145/145 2) 143/145 3) 142/145 4) 136/145 9. Fifteen persons, among whom are A and B, sit at random around a round table. The probability that there are 4 persons between A and B is 1) 1/7 2) 2/7 3) 3/7 4) 4/7 10. If four people are chosen at random, then the probability that no two of them are born on the same day of the week is 1) 30/40 2) 203/225 3) 120/343 4) 6/49 12. A determinant is chosen at random from the set of all determinants of order two with elements 0 and 1 only. The probability that the value of the determinant chosen is positive is 1) 3/8 2) 3/16 3) 1/8 4) 1/16 13. Two cards are drawn at random from a pack of 52 cards. The probability that it is either both are black or both are aces is 1) 4/13 2) 11/13 3) 55/221 4) 15/34 14. If one ticket is randomly selected from tickets numbered from 1 to 30 then the probability that the number on the ticket is a multiple of 5 or 7 is 1) 1/3 2) 2/3 3) 4/3 4) 15/34 15.Two dice are thrown at a time and the sum of the numbers on them is 6. The probability that 10 cards will precede of the dice is 1) 2/5 3) 1/5 3) 2/3 4) 1/3 16. Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is 1) 241/1456 2) 164/4165 3) 451/884 4) 164/3195 17. The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is 1) 4/5 2) 2/5 3) 7/5 4) 9/25 18 Four whole numbers are taken at random and multiplied together. The probability that the product ends in an odd digit other than five is 1) 609/625 2) 16/625 3) 2/5 4) 3/5 19. A speaks truth in 75 percent of the cases and B in 80 percent of the cases. The percentage of the cases of which they likely to contradict each other in stating the same fact is 1) 20% 2) 25% 3) 30% 4) 35% 20. Bag A contains three white and two black balls. Bag B contains two white and four black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is 1) 52/77 2) 76/155 3) 89/198 4) 7/15 KEY: 1)4 2)2 3)3 4)3 5)4 6)4 7)2 8)1 9)1 10)3 12)2 13)3 14)1 15)1 16)2 17)4 18)2 19)4 20)4.