Question

Given that events A and B are independent and that P(A) = 0.8 and P(B|A) = 0.4, then P(A and B) = 0.32.

a. True
b. False

Answer 1

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

P(A) = 0.8

P(B|A) = 0.4

Since A and B are independent events.

Since P(B|A) is given, we will use the formula for "conditional probability":

So, $P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\0.4=\dfrac{P(A\cap B)}{0.8}\\\\0.4\times 0.8=P(A\cap B)}\\\\0.32=P(A\cap B)$

Hence, it is true.

Therefore, Option 'a' is correct.