Question

Two thousand adults were randomly selected and asked whether they had shopped online in the previous week. Their responses are in the table. Are the events F = "is female" and S = "have shopped" independent? Why or why not?

A) Yes; because P(F & S) = P(F) · P(S).
B) No; because P(F & S) ≠ P(F) · P(S)
C) Yes; because P(F & S) = P(F) + P(S)
D) No; because P(F & S) ≠ P(F) + P(S)

I'm pretty sure it's B but I want to make sure.

Answer 1

The answer is B; because P(F & S) ≠ P(F) · P(S).

Explanation:

The reason why is because:

P(F) = 800/2000 = 0.4, P(S) = 800/2000 = 0.4, but P(F & S) = 300/2000 = 0.15.

Also I know it's right because i just did this on USA Testprep. Hahaha

Answer 2

The answer is B.

Explanation:

No; because P(F & S) ≠ P(F) · P(S) P(F) = 800/2000 = 0.4, P(S) = 800/2000 = 0.4, but P(F & S) = 300/2000 = 0.15.