Statistics And Probability Question 508

Question: If $ P(A_1\cup A_2)=1-P(A_1^{c})P(A_2^{c}) $ where c stands for complement, then the events $ A_1 $ and $ A_2 $ are

[MP PET 1989]

Options:

A) Mutually exclusive

B) Independent

C) Equally likely

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ P(A_1\cup A_2)=1-[1-P(A_1)][1-P(A_2)] $ $ =P(A_1)+P(A_2)-P(A_1).P(A_2) $ .