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Class 11 Maths NCERT Solutions For Chapter 16 Probability

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Chapter 16 Probability

Download NCERT Solutions for Class 11 Mathematics

(Link of Pdf file is given below at the end of the Questions List)

In this pdf file you can see answers of following Questions

EXERCISE 16.1


1 to 7, describe the sample space for the indicated experiment.


Question 1.A coin is tossed three times.


Question 2.A die is thrown two times.


Question 3.A coin is tossed four times.


Question 4.A coin is tossed and a die is thrown.


Question 5.A coin is tossed and then a die is rolled only in case a head is shown on the coin


Question 6.2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.


Question 7. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.


Question 8. An experiment consists of recording boy–girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?


Question 9.A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.


Question 10. An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.


Question 11.Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non – defective(N). Write the sample space of this experiment.


Question 12.A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?


Question 13.The numbers 1, 2, 3 and 4 are written separatly on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.


Question 14.An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.


Question 15.A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.


Question 16.A die is thrown repeatedly untill a six comes up. What is the sample space for this experiment?


EXERCISE 16.2


Question 1.A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?


Question 2.A die is thrown. Describe the following events:
(i) A: a number less than 7
(ii) B: a number greater than 7
(iii) C: a multiple of 3
(iv) D: a number less than 4
(v) E: an even number greater than 4
(vi) F: a number not less than 3 Also find A ∪ B, A ∩ B, E ∪ F, D ∩ E, A – C, D – E, F′, E ∩ F′,


Question 3.An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: A: the sum is greater than 8, B: 2 occurs on either die C: the sum is at least 7 and a multiple to 3 Which pairs of these events are mutually exclusive?


Question 4.Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”. Which events are
(i) mutually exclusive?
(ii) simple?
(iii) Compound?


Question 5.Three coins are tossed. Describe
(i) Two events which are mutually exclusive .
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.


Question 6.Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice ≤


Question 5.Describe the events
(i) A′
(ii) not B
(iii) A or B
(iv) A and B
(v) A but not C
(vi) B or C
(vii) B and C
(viii) A ∩ B′ ∩ C′


Question 7. Refer to question 6 above, state true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) A = B′
(iv) A and C are mutually exclusive (v) A and B′ are mutually exclusive. (vi) A′, B′, C are mutually exclusive and exhaustive.

EXERCISE 16.3


Question 1.Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = { } ω1,ω2 ,ω3,ω4 ,ω5 ,ω6 ,ω7


Question 2.A coin is tossed twice, what is the probability that atleast one tail occurs?


Question 3.A die is thrown, find the probability of following events:
(i) A prime number will appear,
(ii) A number greater than or equal to 3 will appear,
(iii) A number less than or equal to one will appear,
(iv) A number more than 6 will appear,
(v) A number less than 6 will appear.


Question 4.A card is selected from a pack of 52 cards .
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is
(i) an ace
(ii) black card.


Question 5.A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is
(i) 3
(ii) 12


Question 6.There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?


Question 7. A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.


Question 8.Three coins are tossed once. Find the probability of getting
(i) 3 heads
(ii) 2 heads
(iii) atleast 2 heads
(iv) atmost 2 heads
(v) no head
(vi) 3 tails
(vii) exactly two tails
(viii) no tail
(ix) atmost two tails


Question 9.If 11 2 is the probability of an event, what is the probability of the event ‘not A’.


Question 10.A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is
(i) a vowel
(ii) a consonan


Question 11.In a lottery, a person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of Winning the prize in the game. [Hint order of the numbers is not important.]


Question 12.Given P(A) = 5 3 and P(B) = 51. Find P(A or B), if A and B are mutually exclusive events.


Question 13.If E and F are events such that P(E) = 4 1 , P(F) = 2 1 and P(E and F) = 8 1 , find
(i) P(E or F),
(ii) P(not E and not F).


Question 14.Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.


Question 15. A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0
Question 6.Determine (i) P(not A), (ii) P(not B) and (iii) P(A or B)


Question 16. In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.


Question 17. In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0. 7. The probability of passing atleast one of them is 0.99. What is the probability of passing both?


Question 18. The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 01. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?


Question 20.In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted neither NCC nor NSS.
(iii) The student has opted NSS but not NCC.


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