Question

Are events "four" and "diamonds" independent events (justify answer)

Answer 1

Here lets say events four is event A and event diamonds is event B

so here probability of event A = Pr(Getting a Four) = 1/13 (as there are 13 cards of any suit and one of them is four)

probability of event B = Pr(Getting a diamond) = 1/4 (as there are 13 cards of diamonds out of 52)

Two events A and B would be independent if

P(A and B) = P(A) P(B)

Here

P(A and B) = P(Getting a four of diamond) = 1/52 [as there is only one four of diamong out of 52]

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

so here

P(A and B) = P(A) P(B)

so these two events are independent.