Question

You draw a card from a deck of
52
cards twice, each time replacing the card. Find the following probabilities (rounded to the nearest thousandths) of observing:

a.) exactly 1 black card.
P(1 black card)=



b.) exactly 1 club. P(1 club)=



c.) exactly 1 two. P(1 two)

Answer 1

a) not black ---> white
so you could have WB or BW
prob(WB or BW) = (1/2)(1/2) + (1/2)(1/2) = 1/2

or, think of it this way:
outcomes are WW, WB, BW, BB for a total of 4 possibilities, both W and B have equal likely outcomes
two of those are the outcomes you want ---> 2/4 = 1/2

b.) exactly 1 club. , let X be non-club
prob(club) = 13/52 = 1/4
prob(X) = 3/4

you want Prob(CX or XC) = (1/4)(3/4) + (3/4)(1/4) = 3/8

do c) following the method of b)