If P(A)=0.4, P(A∪B)=0.7, then the probability of B will be maximum when A and B are: MCQ with Answer and Explanation

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If P(A)=0.4, P(A∪B)=0.7, then the probability of B will be maximum when A and B are:

A. Mutually exclusive

B. B is a subset of A

C. Independent

D. A is a subset of B

Answer: Option D

Solution (By JKExamLibrary)

P(A∪B)=P(A)+P(B)-P(A∩B). To maximize P(B) given P(A∪B)=0.7 and P(A)=0.4, set P(A∩B)=P(A)=0.4 (i.e., A⊂B). Then 0.7=0.4+P(B)-0.4 => P(B)=0.7 max.

This question belongs to: Accountancy and Statistics Statistics

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Practice More Statistics Questions

Question #1 Report Error

Given P(A)=0.4, P(B)=0.5, and A and B are mutually exclusive, P(A∪B) is:

A. 0.9

B. 0.1

C. 0.7

D. 0.2

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Correct Answer: Option A

Explanation:
Mutually exclusive ⇒ P(A∪B) = P(A)+P(B) = 0.4+0.5=0.9.

This question belongs to: Accountancy and Statistics Statistics

Question #2 Report Error

If Yule's Q = 0.8, it indicates:

A. Strong negative association

B. Weak association

C. Independence

D. Strong positive association

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Correct Answer: Option D

Explanation:
Q close to +1 indicates strong positive association.

This question belongs to: Accountancy and Statistics Statistics

Question #3 Report Error

Consider the following pairs: (1) CBR - Per 1000 population, (2) GFR - Per 1000 women aged 15-49, (3) IMR - Per 1000 live births. Which pair is correctly matched?

A. 1, 2 and 3

B. 2 and 3 only

C. 1 and 3 only

D. 1 and 2 only

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Correct Answer: Option A

Explanation:
All three definitions are correct.

This question belongs to: Accountancy and Statistics Statistics

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