Class 11 Mathematics Probability MCQs Set 02

Question: A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Then, the total number of outcomes for this experiment is
a) 40
b) 42
c) 41
d) 43
Answer: b

Question: Two coins (a ₹ 2 coin and a ₹ 5 coin) are tossed once. The total number of elements in sample space is
a) 2
b) 4
c) 3
d) 11
Answer: b

Question: If an event has more than one sample point, then it is called a/an ______.
a) simple event
b) elementary event
c) compound event
d) None of the options
Answer: c

Question: The probability that a patient visiting a dentist will have a tooth extracted is 0.06, the probability that he will have a cavity filled is 0.2, and the probability that he will have a tooth extracted or a cavity filled is 0.23. What is the probability that he will have a tooth extracted as well as a cavity filled?
a) 0.03
b) 0.04
c) 0.05
d) 0.06
Answer: a

Question: The whole sample space S is called _______ event.
a) sure
b) impossible
c) distinct
d) negative
Answer: a

Question: The set A – B denotes the event
a) A and B
b) A or B
c) only A
d) A but not B
Answer: d

Question: When a pair of dice is rolled (one is yellow and the other is green), then
a) total number of elements in sample space is 6 × 6.
b) sample space is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}.
c) both (a) and (b).
d) total number of elements in sample space is 6 + 6.
Answer: a

Question: A coin is tossed once, then the sample space is
a) {H}
b) {T}
c) {H, T}
d) None of the options
Answer: c

Question: Event can be classified into various types on the basis of the ______ they have.
a) experiment
b) sample space
c) elements
d) None of the options
Answer: c

Question: For every event A, there corresponds another event A′ called the ______ of A.
a) complementary event
b) simple event
c) not complementary event
d) None of the options
Answer: a

Question: A coin is tossed twice. If the second throw result in a tail, a die is thrown. Then, the total number of possible outcomes of this experiment is
a) 11
b) 13
c) 14
d) 16
Answer: c

Question: If A and B are mutually exclusive events and P(b) = 1/3, P(A∪ B) =13/21, then P(a) is equal to
a) 1/7
b) 4/7
c) 2/7
d) 5/7
Answer: c

Question: A coin is tossed repeatedly until a tail comes up for the first time. Then, the sample space for this experiment is
a) {T, HT, HTT}
b) {TT, TTT, HTT, THH}
c) {T, HT, HHT, HHHT, HHHHT,……}
d) None of the options
Answer: c

Question: A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Find the probability that it is either red or blue.
a) 2/9
b) 7/9
c) 1/9
d) 4/9
Answer: b

Question: A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. Then, the possible outcomes of this experiment is
a) {RR, BB}
b) {RR, B,B, RR}
c) {BB, R}
d) {RR, RB, BR, BB}
Answer: d

Question: A die is rolled. Let E be the event “die shows 4” and F be the event “die shows an even number”. Then, E and F are
a) mutually exclusive events
b) exhaustive events
c) mutually exclusive and exhaustive events
d) None of the options
Answer: d

Question: When the sets A and B are two events associated with a sample space. Then, event A ∪ B denotes
a) A and B
b) only A
c) A or B
d) only B
Answer: c

Question: If A and B be two events associated with a random experiment such that P(a) = 0.3, P(b) = 0.2 and P(A ∩ B) = 0.1, find P(A∩ B) .
a) 0.1
b) 0.2
c) 0.3
d) 0.4
Answer: a

Question: If A and B are any two events, then P(A ∩ B′) =
a) Pa) + P(B′)
b) Pa) + P(A ∩ B)
c) Pb) – P(A ∩ B)
d) Pa) – P(A ∩ B)
Answer: d

Question: If A and B be two events associated with a random experiment such that P(a) = 0.3, P(b) = 0.2 and P(A ∩ B) = 0.1, find P(A∩B).
a) 0.3
b) 0.1
c) 0.2
d) 1.1
Answer: c

Question: A box contains 1 red and 3 identical blue balls.
Two balls are drawn at random in succession without replacement. Then, the sample space for this experiment is
a) {RB, BR, BB}
b) {R, B, B}
c) {RB}
d) {RB, BR}
Answer: a

Question: A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 yellow and 3 red balls. If it shows head, we throw a die. Then, the sample space for this experiment is
a) S = {TY₁, TY₂, TR₁, TR₂, TR₃, H₁, H₂, H₃, H₄, H₅, H₆}
b) S = {TY₁, TY₂, TR₁, H₁, H₄}
c) S = {Y₁, Y₂}
d) None of the options
Answer: a

Question: Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that only one of them will qualify the examination.
a) 0.11
b) 0.10
c) 0.12
d) 0.13
Answer: a

Question: The total number of elementary events associated to the random experiment of throwing three die together is
a) 210
b) 216
c) 215
d) 220
Answer: b

Question: A and B are two events such that P(a) = 0.54, P(b) = 0.69 and P(A ∩ B) = 0.35.
Find (i) P(A′ ∩ B′) (ii) P(A ∩ B′)
(i) (ii)
a) 0.12 0.19
b) 0.19 0.12
c) 0.13 0.20
d) 0.19 0.18
Answer: a

Question A event which has only X sample point(s) of a sample space, is called simple event. Here, X refers to ______.
a) two
b) three
c) one
d) zero
Answer: c

Question: If A and B are two events, then the set A ∩ B denotes the event
a) A or B
b) A and B
c) only A
d) only B
Answer: b

Question: One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, then the probability that the card drawn is not a diamond.
a) 1/4
b) 1/7
c) 3/4
d) 1/5
Answer: c

Question: The empty set f is called _______ event.
a) sure
b) impossible
c) simple
d) possible
Answer: b

Question: The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive, then the probability of neither A nor B occurring is
a) 0.9
b) 0.7
c) 0.1
d) 0.2
Answer: d

Question: One die of red colour(R), one of white colour(W) and one of blue colour (b) are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Then, the sample space is
a) S = {R₁, R₂, R₃, R₄, R₅, R₆, W₁, W₂, W₃, W₄, W₅, W₆, B₁, B₂, B₃, B₄, B₅, B₆}
b) S = {R₁, R₂, R₃, R₄, R₅, R₆, W₁, W₂, W₄, W₅, B₁,B₃, B₄, B₅, B₆}
c) Both a) and (b)
d) None of the options
Answer: a

Question: An experiment involves rolling a pair of dice.
The following events are recorded.
P : The sum is greater than 9.
Q : 1 occurs on either die.
R : The sum is atleast 8 and a multiple of 3.
Which pair of these events is/are mutually exclusive?
a) P and Q
b) Q and R
c) Both P and Q and Q and R
d) None of the options
Answer: c

Question: If A and B are any two events having P(A∪ B) = 1/2 and P(–A) = 2/3, then the probability of A–∪ B is
a) 1/2
b) 2/3
c) 1/6
d) 1/3
Answer: c

Question: A die is thrown repeatedly until a six comes up. Then, the sample space for this experiment is
a) S = {6, (1, 6), (2, 6), (3, 6)}
b) S = {(6, 1), (6, 2), (6, 4), (6, 6)}
c) infinite number of possibilities occur
d) None of the options
Answer: c

Question: Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment.
A : “the sum is even”.
B : “the sum is a multiple of 3”.
C : “the sum is less than 4”.
D : “the sum is greater than 11”.
Which pair of these events is mutually exclusive?
a) A and B
b) B and C
c) C and D
d) A and C
Answer: c

Assertion & Reasoning Based Questions :

a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
c) Assertion is correct statement but Reason is wrong statement.
d) Assertion is wrong statement but Reason is correct statement..

Question:
Assertion : The probability of drawing either an ace or a king from a pack of cards in a single draw is 2/13.
Reason : For two events A and B which are not mutually exclusive, P(A ∪ B) = P(a) + P(b) – P(A ∩ B).
Answer: b

Question: Consider the experiment of rolling a die. Then, sample space is S = { 1, 2, 3, 4, 5, 6}
Assertion : The event E : “the number appears on the die is a multiple of 7”, is an impossible event.
Reason : The event F : “the number turns up is odd or even”, is a sure event.
Answer: b

Question:
Assertion : If sample space of an experiment is S = {1, 2, 3, 4, 5, 6} and the events A and B are defined as
A : “a number less than or equal to 3 appears”
B : “a number greater than or equal to 3 appears”, then A and B are exhaustive events.
Reason : Events are exhaustive if atleast one of them necessarily occur whenever the experiment is performed.
Answer: a

Question:
Assertion : A coin is tossed. If it shows head, we draw a ball from a bag consisting of 3 brown and 4 red balls; if it shows tail we throw a die, then the sample space of this experiment is S = {HB₁, HB₂, HB₃, HR₁, HR₂, HR₃, HR₄, T₁, T₂, T₃, T₄, T₅, T₆}
Reason : Consider the experiment in which a coin is tossed repeatedly until a head comes up, then the sample space is S = {H, TH, TTH, TTTH,……..}
Answer: b

Question:
Assertion : A coin is tossed and then a die is rolled only in case a head is shown on the coin.
The sample space for the experiment is S = {H₁, H₂, H₃, H₄, H₅, H₆, T}
Reason : 2 boys and 2 girls are in room X, and 1 boy and 3 girls are in room Y. Then, the sample space for the experiment in which a room is selected and then a person, is
S = {XB₁, XB₂, XG₁, XG₂, YB₃, YG₃, YG₄, YG₅} where Bi, denote the boys and Gj, denote the girls.
Answer: b