Find P(HIG)

Question

A card is drawn at random from a standard 52-card deck.Events G and H are G=the drawn card is black, H=the drawn card is divisible by 5(FACE CARDS are not valued.

 

Find p(HlG)

Test H and G for indepence

 

Answer 1

So conditional probability

P(H|G) = P(H and G)/P(G)

 

P(G) = probability card drawn is black = 1/2 (26 black cards in 52 deck)

P(H|G) = probability card is divisible by 5 given it is a black card. There are 26 black cards and only cards divisble by 5 are {5 clubs, 10 clubs, 5 spades, 10 spades} thus P(H|G) = 4/26 = 2/13

 

This means 

P(H and G) = P(G)P(H|G) = (1/2)*(2/13) = 1/13

 

To test for independence we need P(H) 

We see P(H) = 8/52 = 2/13.

 

So P(H and G) = 1/13 = P(H)P(G) hence independent