Probability Of Random Experiments

PYQ 2023

medium

mathematics ID: cuet-ug-

For two events A and B Match List I with List II List I List II A. I. B. and II. C. III. A and B are independent events D. IV. A and B are mutually exclusive events Choose the correct answer from the options given below:

List I	List II
A. $P%20(%5Cbar%7B%5Cbigwedge%7D%20%5Ccap%20%5Cbar%7BB%7D)%20%3D%20P(%5Cbar%7B%5Cbigwedge%7D)%20.%20P(%5Cbar%7BB%7D)$	I. $P(A%2FB)%20%5Cgeq%20P(A)$
B. $A%20%5Csubset%20B$ and $P(B)%20%5Cneq0$	II. $P(A)%20%3D%20P(B)$
C. $P(A%20%5Cbigcup%20B)%20%3D%20P(A)%20%2B%20P(B)$	III. A and B are independent events
D. $P(A%7CB)%20%3D%20P%20(B%7CA)$	IV. A and B are mutually exclusive events

A-III, В-II, C-IV, D-I

А-III, В-I, C-IV, D-II

A-IV, B-II, C-III, D-I

A-IV, B-I, C-III, D-II

Correct Option: (2)

Let's match List I with List II using the properties of probability: List I List II A. III. A and B are independent events B. and I. C. IV. A and B are mutually exclusive events D. II. Explanation: Option A: For two events A and B, if, this describes the condition for two independent events. Option B: If and, then because all parts of A are within B. Option C: If, this indicates A and B are mutually exclusive events, as they do not overlap. Option D: means both events have the same probability, indicating . Therefore, the matching is А-III, В-I, C-IV, D-II.

List I	List II
A. $P%20(%5Cbar%7B%5Cbigwedge%7D%20%5Ccap%20%5Cbar%7BB%7D)%20%3D%20P(%5Cbar%7B%5Cbigwedge%7D)%20.%20P(%5Cbar%7BB%7D)$	III. A and B are independent events
B. $A%20%5Csubset%20B$ and $P(B)%20%5Cneq%200$	I. $P(A%2FB)%20%5Cgeq%20P(A)$
C. $P(A%20%5Cbigcup%20B)%20%3D%20P(A)%20%2B%20P(B)$	IV. A and B are mutually exclusive events
D. $P(A%7CB)%20%3D%20P(B%7CA)$	II. $P(A)%20%3D%20P(B)$

PYQ 2023

medium

mathematics ID: cuet-ug-

Let a pair of dice be thrown and the random variable X be the sum of numbers on the two dice. Then. Match List I with List II. List I List II A. P (X = 2) I. B. P (X = 4) II. C. P (X - 5) III. D. P (X - 6) IV. Choose the correct answer from the options given below:

А-I, В-II, С-III, D-IV

А-II, В-III, С-IV, D-I

A-III, B-IV, C-I, D-II

A-IV, B-I, C-II, D-III

Correct Option: (3)

A pair of dice can be thrown to get various sums ranging from 2 to 12. The random variable X represents this sum. We will calculate the probabilities for these sums and match them with the options provided in List II. P(X=2) : This occurs only when both dice show 1, i.e., (1,1). The probability is thus . P(X=4) : The combinations are (1,3), (2,2), and (3,1). The probability is . P(X=5) : The combinations are (1,4), (2,3), (3,2), and (4,1). The probability is . P(X=6) : The combinations are (1,5), (2,4), (3,3), (4,2), and (5,1). The probability is . List I List II A. P(X=2) III. B. P(X=4) IV. C. P(X=5) I. D. P(X=6) II. Thus, the correct matching is A-III, B-IV, C-I, D-II .

Chapter Questions
2 MCQs