These Probability Class 11 Important Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Probability Class 11 Important Questions And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Probability Class 11 Important Questions And Answers

1. A dice is tossed for 4 times. The probability of getting 1 for a minimum 1 time is

(A) 617/1269

(B) 617/1296

(C) 671/1269

(D) 671/1296

**Answer:** 671/1296

2. A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, then the probability that it is rusted or a nail is

(A) 3/16

(B) 5/16

(C) 11/16

(D) 14/16

**Answer:** 11/16

3. Seven white balls and three black balls are randomly placed in a row . The probability that no two black balls are placed adjacently equals

(A) 1/2

(B) 7/15

(C) 2/15

(D) 1/3

**Answer:** 7/15

4. When a coin is tossed 8 times getting a head is a success. Then the probability that at least 2 heads will occur is

(A) 247/265

(B) 73/256

(C) 247/256

(D) 27/256

**Answer:** 247/256

5. The probability of getting the number 6 at least once in a regular die if it can roll it 6 times?

(A) 1 – (5/6)^{6}

(B) 1 – (1/6)^{6}

(C) (5/6)^{6}

(D) (1/6)^{6}

**Answer:** 1 – (5/6)^{6}

6. A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year

(A) e^{-1/2}/2

(B) e-^{-1/2}/4

(C) e-^{-1/2}/8

(D) none of these

**Answer:** e-^{-1/2}/8

7. 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

(A) 2/9

(B) 1/9

(C) 8/9

(D) 7/9

**Answer:** 1/9

8. Two dice are thrown the events A, B, C are as follows A: Getting an odd number on the first die. B: Getting a total of 7 on the two dice. C: Getting a total of greater than or equal to 8 on the two dice. Then AUB is equal to

(A) 15

(B) 17

(C) 19

(D) 21

**Answer:** 21

9. The probability that in a random arrangement of the letters of the word INSTITUTION the three T are together is

(A) 0.554

(B) 0.0554

(C) 0.545

(D) 0.0545

**Answer:** 0.0545

10. Two unbiased dice are thrown. The probability that neither a doublet nor a total of 10 will appear is

(A) 3/5

(B) 2/7

(C) 5/7

(D) 7/9

**Answer:** 7/9

11. A bag contains 5 brown and 4 white socks . A man pulls out two socks. The probability that both the socks are of the same colour is

(A) 9/20

(B) 2/9

(C) 3/20

(D) 4/9

**Answer:** 4/9

12. The probability of getting 53 Sundays in a leap year is

(A) 1/7

(B) 2/7

(C) 3/7

(D) None of these

**Answer:** 2/7

13. Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is

(A) 1/5

(B) 4/5

(C) 1/30

(D) 5/9

**Answer:** 5/9

14. Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is

(A) 1/3

(B) 1/6

(C) 2/7

(D) 1/2

**Answer:** 2/7

15. While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours

(A) 29/52

(B) 1/2

(C) 26/51

(D) 27/51

**Answer:** 26/51

16. In a non-leap year, the probability of having 53 Tuesdays or 53 Wednesdays is

(A) 1/7

(B) 2/7

(C) 3/7

(D) none of these

**Answer:** 2/7

17. Two fair dice are tossed. Let X be the event that the first die shows an even number, and Y be the event that the second die shows an odd number. The two events X and Y are

(A) mutually exclusive

(B) independent and mutually exclusive

(C) dependent

(D) Independent

**Answer:** Independent

18. On his vacation, Rahul visits four cities (A, B, C, and D) in a random order. The probability that he visits A first and B last is

(A) 1/2

(B) 1/6

(C) 1/10

(D) 1/12

**Answer:** 1/12

19. The probabilities 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 40% chance of passing in exactly two . Which of the following relations are true ?

(A) p + m + c = 19/20

(B) p + m + c = 27/20

(C) pmc = 1/10

(D) pms = 1/4

**Answer:** p + m + c = 27/20

20. Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is diamond then the probability that the lost cards were both hearts is

(A) 143/1176

(B) 143/11760

(C) 143/11706

(D) 134/11760

**Answer:** 143/11760