Question

Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities.

a) Assume the cards are drawn without replacement. Find the probability of drawing 2 tens.
b) Assume the cards are drawn with replacement. Find the probability of drawing 2 tens.
a. The probability of drawing 2 tens without replacement is
(Simplify your answer.)
b. The probability of drawing 2 tens with replacement is
(Simplify your answer.)

Answer 1

Explanation:

WITHOUT replacement of first card drawn:

P(a 10 is drawn) = 13/52 = 1/4

P(the next draw is a 10) = 12/52 = 3/13

P(drawing two 10s without replacement of the first draw) = (1/4)(3/13) = 3/52

WITH replacement of first card:

P(two 10s are drawn) = P(first card is a 10)*P(first card is a 10) = (4/13)(4/13) =

16/169