Face card and club card independent

Question

Are the events "the card is a face" and "the card is a club" independent? How do I know?

Answer 1

Bryanne,

To check if two events, A and B are independent calculate P(A), P(B), and P(A ∩ B), and then check if

P(A ∩ B) equals P(A)P(B). If so, they are independent.

A=the card is a face

B=the card is a club

P(A)= 16/52 = 4/13

P(B)=13/52 = 1/4

P(A ∩ B)=4/52 , since it represents the cards that are face and club

P(A)P(B) = 4/13 *1/4 = 1/13, which is not equal to P(A ∩ B)=4/52 , so they are not independent.