NCERT Solutions Class 11 Mathematics Chapter 15 Probability Download In Pdf

Chapter 16 Probability Download in pdf

**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.

**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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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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