Class 11
Dashboard
Mathematics
Probability
NCERT Solutions
NCERT Solutions
Probability
38 Solutions
Exercise:
All Exercises
Exercise 14.1
Exercise 14.2
Miscellaneous Exercise on Chapter 14
Q1
Exercise 14.1
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?
Q2
Exercise 14.1
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
,
B
∪
C
,
E
∩
F
,
D
∩
E
,
A
−
C
,
D
−
E
,
E
∩
F
′
,
F
′
A \cup B, A \cap B, B \cup C, E \cap F, D \cap E, A - C, D - E, E \cap F', F'
A
∪
B
,
A
∩
B
,
B
∪
C
,
E
∩
F
,
D
∩
E
,
A
−
C
,
D
−
E
,
E
∩
F
′
,
F
′
Q3
Exercise 14.1
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 of 3. Which pairs of these events are mutually exclusive?
Q4
Exercise 14.1
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?
Q5
Exercise 14.1
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.
Q6
Exercise 14.1
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
≤
5
\leq 5
≤
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
′
A \cap B' \cap C'
A
∩
B
′
∩
C
′
Q7
Exercise 14.1
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.
Q1
Exercise 14.2
Which of the following can not be valid assignment of probabilities for outcomes of sample Space
S
=
{
ω
1
,
ω
2
,
ω
3
,
ω
4
,
ω
5
,
ω
6
,
ω
7
}
S=\{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}
S
=
{
ω
1
,
ω
2
,
ω
3
,
ω
4
,
ω
5
,
ω
6
,
ω
7
}
| Assignment |
ω
1
\omega_{1}
ω
1
|
ω
2
\omega_{2}
ω
2
|
ω
3
\omega_{3}
ω
3
|
ω
4
\omega_{4}
ω
4
|
ω
5
\omega_{5}
ω
5
|
ω
6
\omega_{6}
ω
6
|
ω
7
\omega_{7}
ω
7
|
|---|---|---|---|---|---|---|---|
| (a) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
| (b) |
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
1
7
\frac{1}{7}
7
1
|
| (c) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
| (d) | -0.1 | 0.2 | 0.3 | 0.4 | - 0.2 | 0.1 | 0.3 |
| (e) |
1
14
\frac{1}{14}
14
1
|
2
14
\frac{2}{14}
14
2
|
3
14
\frac{3}{14}
14
3
|
4
14
\frac{4}{14}
14
4
|
5
14
\frac{5}{14}
14
5
|
6
14
\frac{6}{14}
14
6
|
15
14
\frac{15}{14}
14
15
|
Q2
Exercise 14.2
A coin is tossed twice, what is the probability that atleast one tail occurs?
Q3
Exercise 14.2
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.
Q4
Exercise 14.2
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.
Q5
Exercise 14.2
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
Q6
Exercise 14.2
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?
Q7
Exercise 14.2
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.
Q8
Exercise 14.2
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
Q9
Exercise 14.2
If
2
11
\frac{2}{11}
11
2
is the probability of an event, what is the probability of the event 'not A '.
Q10
Exercise 14.2
A letter is chosen at random from the word 'ASSASSINATION'. Find the probability that letter is (i) a vowel (ii) a consonant
Q11
Exercise 14.2
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.]
Q12
Exercise 14.2
Check whether the following probabilities P(A) and P(B) are consistently defined
(i)
P
(
A
)
=
0.5
,
P
(
B
)
=
0.7
,
P
(
A
∩
B
)
=
0.6
P(A) = 0.5, P(B) = 0.7, P(A \cap B) = 0.6
P
(
A
)
=
0.5
,
P
(
B
)
=
0.7
,
P
(
A
∩
B
)
=
0.6
(ii)
P
(
A
)
=
0.5
,
P
(
B
)
=
0.4
,
P
(
A
∪
B
)
=
0.8
P(A) = 0.5, P(B) = 0.4, P(A \cup B) = 0.8
P
(
A
)
=
0.5
,
P
(
B
)
=
0.4
,
P
(
A
∪
B
)
=
0.8
Q13
Exercise 14.2
Fill in the blanks in following table:
| | P(A) | P(B) | P(A
∩
\cap
∩
B) | P(A
∪
\cup
∪
B) |
|---|---|---|---|---|
| (i) |
1
3
\frac{1}{3}
3
1
|
1
5
\frac{1}{5}
5
1
|
1
15
\frac{1}{15}
15
1
| ... |
| (ii) | 0.35 | ... | 0.25 | 0.6 |
| (iii) | 0.5 | 0.35 | ... | 0.7 |
Q14
Exercise 14.2
Given
P
(
A
)
=
3
5
P(A) = \frac{3}{5}
P
(
A
)
=
5
3
and
P
(
B
)
=
1
5
P(B) = \frac{1}{5}
P
(
B
)
=
5
1
. Find
P
(
A
or
B
)
P(A \text{ or } B)
P
(
A
or
B
)
, if A and B are mutually exclusive events.
Q15
Exercise 14.2
If E and F are events such that
P
(
E
)
=
1
4
,
P
(
F
)
=
1
2
P(E) = \frac{1}{4}, P(F) = \frac{1}{2}
P
(
E
)
=
4
1
,
P
(
F
)
=
2
1
and
P
(
E
and
F
)
=
1
8
P(E \text{ and } F) = \frac{1}{8}
P
(
E
and
F
)
=
8
1
, find (i)
P
(
E
or
F
)
P(E \text{ or } F)
P
(
E
or
F
)
, (ii)
P
(
not
E
and not
F
)
P(\text{not } E \text{ and not } F)
P
(
not
E
and not
F
)
.
Q16
Exercise 14.2
Events E and F are such that
P
(
not
E
or not
F
)
=
0.25
P(\text{not } E \text{ or not } F) = 0.25
P
(
not
E
or not
F
)
=
0.25
, State whether E and F are mutually exclusive.
Q17
Exercise 14.2
A and B are events such that
P
(
A
)
=
0.42
,
P
(
B
)
=
0.48
P(A) = 0.42, P(B) = 0.48
P
(
A
)
=
0.42
,
P
(
B
)
=
0.48
and
P
(
A
and
B
)
=
0.16
P(A \text{ and } B) = 0.16
P
(
A
and
B
)
=
0.16
. Determine (i)
P
(
not
A
)
P(\text{not } A)
P
(
not
A
)
, (ii)
P
(
not
B
)
P(\text{not } B)
P
(
not
B
)
and (iii)
P
(
A
or
B
)
P(A \text{ or } B)
P
(
A
or
B
)
Q18
Exercise 14.2
In Class XI of a school
40
%
40\%
40%
of the students study Mathematics and
30
%
30\%
30%
study Biology.
10
%
10\%
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.
Q19
Exercise 14.2
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 0.95 . What is the probability of passing both?
Q20
Exercise 14.2
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 0.1 . If the probability of passing the English examination is 0.75 , what is the probability of passing the Hindi examination?
Q21
Exercise 14.2
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.
Q1
Miscellaneous Exercise on Chapter 14
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that (i) all will be blue? (ii) atleast one will be green?
Q2
Miscellaneous Exercise on Chapter 14
4 cards are drawn from a well - shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Q3
Miscellaneous Exercise on Chapter 14
A die has two faces each with number '1', three faces each with number '2' and one face with number '3'. If die is rolled once, determine
(i)
P(2)
(ii)
P(1 or 3)
(iii)
P(not 3)
Q4
Miscellaneous Exercise on Chapter 14
In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c) 10 tickets.
Q5
Miscellaneous Exercise on Chapter 14
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that
(a)
you both enter the same section?
(b)
you both enter the different sections?
Q6
Miscellaneous Exercise on Chapter 14
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Q7
Miscellaneous Exercise on Chapter 14
A and B are two events such that
P
(
A
)
=
0.54
,
P
(
B
)
=
0.69
P(A) = 0.54, P(B) = 0.69
P
(
A
)
=
0.54
,
P
(
B
)
=
0.69
and
P
(
A
∩
B
)
=
0.35
P(A \cap B) = 0.35
P
(
A
∩
B
)
=
0.35
. Find (i)
P
(
A
∪
B
)
P(A \cup B)
P
(
A
∪
B
)
(ii)
P
(
A
′
∩
B
′
)
P(A' \cap B')
P
(
A
′
∩
B
′
)
(iii)
P
(
A
∩
B
′
)
P(A \cap B')
P
(
A
∩
B
′
)
(iv)
P
(
B
∩
A
′
)
P(B \cap A')
P
(
B
∩
A
′
)
Q8
Miscellaneous Exercise on Chapter 14
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:
S. No.
Name
Sex
Age in years
1.
Harish
M
30
2.
Rohan
M
33
3.
Sheetal
F
46
4.
Alis
F
28
5.
Salim
M
41
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Q9
Miscellaneous Exercise on Chapter 14
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?
Q10
Miscellaneous Exercise on Chapter 14
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
More from this chapter
Chapter overview
Important Points
Practice Questions
Flashcards