Consider the following experiment Three cards are drawn from

Consider the following experiment. Three cards are drawn from a standard deck of 52 cards, one after the other. Before the second card is drawn, the first card is put back in the deck and the deck is re-shuffled. Before the third card is drawn, the second card is put back in the deck and the deck is re-shuffled. Find the probability that all three cards will be in the suit of hearts. Find the probability of not getting all three cards in the suit of hearts. Find the probability of not getting any cards in the suit of hearts.

Solution

Pack of 52 cards, 3 cards are drawn without replacement = ( 52 C 1) ^ 3

a)
Drawing the three cards will be in the suit of hearts = ( 13 ) ^ 3
P( Drawing all 3 cards ) = ( 13 ) ^ 3 / ( 52 ) ^ 3 = 0.015625

b)
P( Drawing all 3 cards of not Hearts) = 1 - ( 13 ) ^ 3 / ( 52 ) ^ 3 = 1 - 0.015625 = 0.9843