Question

Three cards are drawn with replacement from a standard deck of 5252 cards. Find the the probability that the first card will be a diamond, the second card will be a red card, and the third card will be a ten. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

P(first card is diamond) = n(number of diamond cards)/n(total cards)

P(first card is diamond) = 13/52 = 1/4

total cards remaining = 51

diamonds remaining = 12

red cards remaining = 25

P(second card is red) = n(red cards remaining)/n(total cards remaining)

P(second card is red) = 25/51

red cards remaining = 24

total cards remaining = 50

10's remaining = 4

P(third card is 10) = n(10's remaining)/(cards remaining)

P(third card is 10) = 4/50 = 2/25

P(required) = P(first card is diamond) * P(second card is red) * P(third card is 10)

P(required) =

P(required) =

P(required) = 1/102 = 0.009804