Class 11 Mathematics Probability MCQs Set 16

Question. A car is parked by a driver amongst 25 cars in a row, not at either end. When he returns he finds that 10 places are empty. The probability that both the neighbouring places of drivers car are vacant is
(a) 9/92
(b) 15/92
(c) 21/92
(d) 27/92
Answer: (b) 15/92

Question. If four dice are thrown together, then the probability that the sum of the numbers appearing on them is 13 is
(a) \( \frac{5}{216} \)
(b) \( \frac{11}{216} \)
(c) \( \frac{35}{324} \)
(d) \( \frac{11}{432} \)
Answer: (c) \( \frac{35}{324} \)

Question. A number 'n' is chosen at random from S = {1, 2, 3, ...., 50}. Let
\( A = \left\{ n \in S : n + \frac{50}{n} > 27 \right\} \),
\( B = \{ n \in S : n \text{ is a prime} \} \) and
\( C = \{ n \in S : n \text{ is a square} \} \). The correct order of their probabilities is
(a) P(A) < P(B) < P(C)
(b) P(A) > P(B) > P(C)
(c) P(B) < P(A) < P(C)
(d) P(A) > P(C) > P(B)
Answer: (b) P(A) > P(B) > P(C)

Question. An unbiased coin is tossed to get 2 points for turning up a head and one point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting
I : a total of odd no. of points is 2/3
II : a total of 4 or 5 is 3/4
Which of the above statements is / are correct
(a) I only
(b) II only
(c) both I and II
(d) neither I nor II
Answer: (b) II only

Question. A problem is given to two students A and B whose chances of solving it are \( \frac{1}{3}, \frac{1}{5} \) respectively then
                                      LIST-I                                            ​​​​​​​LIST-II 
A) probability that the problem is solved is                    1) 7/15
B) probability that the problem not solved is                 2) 4/15
C) probability that the problem solved by A only is        3) 6/15
D) probability that the problem solved by B only is       ​​​​​​​4) 2/15
                    ​​​​​​​                      ​​​​​​​                      ​​​​​​​                      5) 8/15
The correct match for LIST-I from LIST-II is
    A B C D
(a) 2 1 5 4
(b) 3 5 1 4
(c) 1 5 2 4
(d) 2 1 5 3
Answer: (c) 1 5 2 4

Question. A, B are two events in a random experiment such that 0 < P (A) < 1 and P(B) \( \neq \) 1.
Assertion (A) :- \( P\left(\frac{A}{B^c}\right) = \frac{P(A) - P(A \cap B)}{1 - P(B)} \)
Reason (R) :- \( P\left(\frac{A}{B}\right) = \frac{P(A \cap B)}{P(B)} \)
(a) both A and R are true and R is the correct explanation of A
(b) both A and R are true and R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
Answer: (a) both A and R are true and R is the correct explanation of A

Question. If A,B,C are three independent events of an experiment such that \( P(A \cap B^c \cap C^c) = \frac{1}{4} \), \( P(A^c \cap B \cap C^c) = \frac{1}{8} \), \( P(A^c \cap B^c \cap C^c) = \frac{1}{4} \) then the increasing order of P(A), P(B) and P(C)
(a) P(C) < P(B) < P(A)
(b) P(B) < P(A) < P(C)
(c) P(A) < P(C) < P(B)
(d) P(B) < P(C) < P(A)
Answer: (a) P(C) < P(B) < P(A)

Question. The probability that Australia wins a match against India in a cricket match is 1/3. India and Australia play 3 matches
I. The probability that Australia wins atleast one match is 4/27
II : The probability that Australia looses all the three matches is 8/27
Which of the above statements is correct
(a) I only
(b) II only
(c) both I and II
(d) neither I nor II
Answer: (b) II only

Question. I : A single die is rolled twice in succession. The probability that the number showing on the second toss is greater than that on the first rolling is 4/27.
II : The probability that a boy gets a scholarships is 0.8 and another boy B is 0.9. the probability that atleast one of them gets the scholarship is 0.98. Which of the above statements is true
(a) I only
(b) II only
(c) both I and II
(d) neither I nor II
Answer: (b) II only

Question. A bag X contains 4 white and 2 black balls. Another bag Y contains 3 white and 4 black balls. A bag is selected at random and a ball is drawn at random from it.
I. the probability that the ball drawn is white is 17/42
II. The probability that the ball drawn is black is 19/42
Which of the above statements is correct
(a) only I
(b) only II
(c) both I and II
(d) neither I nor II
Answer: (b) only II

Question. An electrical shopkeeper purchases bulbs from three manufacturers A, B, C. He purchases 25% of his stock from A, 45% from B and 30% from C. In the past purchases he found 2% of C's bulbs, 1% of B's bulbs, 1% of A's bulbs were defective. Assuming that, the shopkeeper chooses a bulb and found it to be defective
                      ​​​​​​​                      LIST-I                      ​​​​​​​                      ​​​​​​​                      ​​​​​​​                      LIST-II
A) The probability of choosing A and purchasing a defective bulb from it is                      1) 0.0025
B) The probability of choosing B and purchasing a defective bulb from it is                      2) 0.0045
C) The probability of choosing C and purchasing a defective bulb from it is                      3) 0.0060
D) The probability that the defective bulb was purchased from C is                                  ​​​​​​​4) 0.65
                                                                                                                                            5) 0.46​​​​​​​
The correct Match for LIST-I from LIST-II is
   ​​​​​​​ A B C D
(a) 4 5 2 3
(b) 5 2 3 1
(c) 2 3 1 5
(d) 1 2 3 5
Answer: (d) 1 2 3 5

Question. Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. p = the probability that exactly one of A and B occurs; q = the probability that neither A or B occurs; r = the probability that A occurs and B does not occur. Which of the following is true
(a) 2q < 5r < p
(b) p < 5r < q
(c) 4r < p < q
(d) p < 5r < 2q
Answer: (d) p < 5r < 2q

Question. Two dice are thrown p = the probability of getting a number always greater than 4 on the second die; q = the probability of getting a sum 10 on the two dice and r = the probability of getting a sum which is a perfect square. Arrange the probabilities in increasing order of magnitude
(a) p, q, r
(b) q, r, p
(c) r, p, q
(d) r, q, p
Answer: (b) q, r, p

Question. p = probability for a leap year to have 52 mondays and 52 wednesdays; q = probability for a non-leap year to have 53 sundays; r = probability of the month February in a leap year to have 5 sundays or 5 saturdays. Then
(a) p < q < r
(b) q < r < p
(c) r < q < p
(d) q < p < r
Answer: (b) q < r < p

Question. A box contains 2 red, 3 blue and 4 black balls, 3 balls are drawn at random from the box. p = the probability for the balls to be of different colours; q = the probability for 2 balls of the same colour and the third of different colour; r = the probability for all the 3 balls to be of the same colour. Arrange them in the decreasing order of magnitude
(a) p, q, r
(b) q, r, p
(c) q, p, r
(d) r, q, p
Answer: (c) q, p, r

Question. A and B be two independent events of a sample space such that P(A) = 0.2, P(B) = 0.5
​​​​​​​         LIST-I                   ​​​​​​​LIST-II   
A) P(B/A)                      1) 0.2
B) P(A/B)                      ​​​​​​​2) 0.1
C) \( P(A \cap B) \)        3) 0.3
D) \( P(A \cup B) \)        4) 0.6
              ​​​​​​​          ​​​​​​​             5) 0.5
The correct match for List-I from List-II
   ​​​​​​​  A B C D
(a) 4 5 3 1
(b) 5 1 2 4
(c) 3 1 2 4
(d) 2 1 4 5
Answer: (b) 5 1 2 4

Question. A, B are two events of a sample space such that \( P(A) = \frac{1}{3}, P(B) = \frac{1}{2}, P(A \cap B) = \frac{2}{15} \)
     LIST-I             ​​​​​​​            LIST-II    ​​​​​​​
A) P(A/B) =                     1) 3/5
B) P(B/A) =                     2) 1/2
C) \( P(A'/B') = \)             3) 4/15
D) \( P(B'/A') = \)             4) 2/5
             ​​​​​​​             ​​​​​​​             5) 9/20
The correct match for LIST-I from LIST-II is
   ​​​​​​​  A B C D
(a) 4 3 2 1
(b) 5 4 3 2
(c) 4 3 2 5
(d) 3 4 1 5
Answer: (d) 3 4 1 5

Question. A husband and wife appear in interview for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. Let a = prob. that both of them will be selected; b = Prob. that none of them will be selected and c = Prob. that only one of them will be selected. Then we have
(a) a < c < b
(b) a < b < c
(c) b < a < c
(d) c < a < b
Answer: (a) a < c < b

Question. A lot contains 50 defective and 50 non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events A, B, C are defined as A = {the first bulb is defective}, B = {the second bulb is non defective}, C = {the two bulbs are both defective or both non defective}. Then
(i) A, B, C are pair wise independent
(ii) A, B, C are independent
(a) only (i) is true
(b) (i) and (ii) are true
(c) only (ii) is true
(d) (i) and (ii) are false
Answer: (a) only (i) is true

Question. Three boxes A, B, C contain balls as shown below
White Red Black
A 2 2 1
B 3 4 2
C 4 2 3
A die is thrown to decide which box is to be chosen. A is chosen if 1 or 2 turns up; B is chosen if 3 or 4 turns up; C is chosen if 5 or 6 turns up. Having chosen the box, a ball is chosen at random from it
I. Probability for the ball to be red is 16/44
II : If the drawn ball is of red colour, the probability that it is from box B is 5/8.
Which of the above statement(s) is/are correct
(a) I only
(b) II only
(c) both I and II
(d) neither I nor II
Answer: (d) neither I nor II

Question. An urn A contains 2 white and 3 black balls. Another urn B contains 3 white and 4 black balls. Out of these two urns, one is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability
I. that it is from urn A is 21/40
II. that is from urn B is 20/41
Which of the following statements is correct
(a) I only
(b) II only
(c) both I and II
(d) neither I nor II
Answer: (b) II only

Question. By rolling a die the following events are considered. \( E_1 \) = {5, 3, 1}, \( E_2 \) = {3, 2}, \( E_3 \) = {5, 4, 3, 2}. The arrangement of the following probabilities
A : \( P(E_1 / E_2) \)
B : \( P(E_1 \cup E_3) \)
C : \( P(E_1 \cap E_3) \)
D: \( P(E_2 \cap E_1) \)
in the descending order is
(a) B, A, C, D
(b) D, C, A, B
(c) C, B, A, D
(d) B, A, D, C
Answer: (a) B, A, C, D

Question. Consider the system of equations
\( ax + by = 0 \), \( cx + dy = 0 \) where \( a,b,c,d \in \{0,1\} \)
Statement - I The probability that the system of equations has a unique solution is 3/8.
Statement - II The probability that the system has a solution is 1.
(a) Statement - I and Statement - II are true Statement - II is not a correct explnation for statement -I
(b) Statement - I and Statement - II are true Statement - II is correct explnation for statement -I
(c) Statement - I is true Statement - II is not true
(d) Statement - I is not true Statement - II is true.
Answer: (a) Statement - I and Statement - II are true Statement - II is not a correct explnation for statement -I