If P(A) = 0.6, P(B) = 0.7, and P(A ∪ B) = 0.9, then P(A ∩ B) is: MCQ with Answer and Explanation

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If P(A) = 0.6, P(B) = 0.7, and P(A ∪ B) = 0.9, then P(A ∩ B) is:

A. 0.2

B. 0.4

C. 0.3

D. 0.5

Answer: Option B

Solution (By JKSSB Mock Tests)

By addition theorem: P(A∪B) = P(A) + P(B) - P(A∩B) → 0.9 = 0.6 + 0.7 - P(A∩B) → P(A∩B) = 1.3 - 0.9 = 0.4.

This question belongs to: Accountancy and Statistics Statistics

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Practice More Statistics Questions

Question #1

Given N=100, (A)=40, (B)=30. The expected frequency of (AB) under independence is:

A. 30

B. 20

C. 40

D. 12

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Correct Answer: Option D

Explanation:
Expected (AB) = (A)×(B)/N = 40×30/100 = 12.

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Question #2

For two events, P(A)=0.4, P(B)=0.3, and P(A∩B)=0.12. Which of the following is true?

A. A and B are mutually exclusive.

B. A and B are independent.

C. P(A∪B)=0.52.

D. A and B are complementary.

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Correct Answer: Option B

Explanation:
0.4×0.3=0.12, so independent. Mutually exclusive would need 0. P(A∪B)=0.4+0.3-0.12=0.58.

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Question #3

What is the primary advantage of the Weighted Arithmetic Mean over the Simple Arithmetic Mean?

A. It is easier to calculate

B. It ignores extreme values

C. It can be calculated for qualitative data

D. It gives appropriate importance to different items based on their significance

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Correct Answer: Option D

Explanation:
Weighted mean assigns weights proportional to the relative importance of items, providing a more accurate average.

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