problem solving
A coin is flipped one time. One card is then drawn at random from a deck containing only 13 cards of 1 suit. What is the probability that the card drawn is higher than a 6 and an odd number card (with a Jack = 11, Queen = 12 and King = 13) given that the coin flipped is heads and the card is a face card?
Solution
S = {(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(H,7),(H,8),(H,9),(H,10),(H,11),(H,12),(H,13),(T,1),(T,2),(T,3),(T,4),(T,5),(T,6),(T,7),(T,8),(T,9),(T,10),(T,11),(T,12),(T,13)}
Total # of outcomes = 26
Card Higher Than Six and Odd = A = {(H,7),(H,9),(H,11),(H,13),(T,7),(T,9),(T,11),(T,13)}
Coin flipped is heads and the card is a face card = B = {(H,11),(H,12),(H,13)}
P(AnB) = {(H,11),(H,13)}
P(A|B) = P(AnB)/P(B) = (2/26)/(3/26) = 2/3
