Question

There are two 7s (of hearts and spades) and two 8s (of hearts and spades) in a deck of cards. The deck has no other cards. Emma draws two cards from this deck and says “I have a 7”. What is the probability of Emma having both 7s? What if she says “I have a 7 of hearts”?

Answer 1

If two cards are drawn then possible outcomes (hearts 7, spades 7),(hearts 7, hearts 8),(hearts 7, Spades 8),(spades 7, hearts 8),(spades 7 , spades 8),(hearts 8, Spades 8)

Favorable outcomes of at least one 7 are (hearts 7, spades 7),(hearts 7, hearts 8),(hearts 7, Spades 8),(spades 7, hearts 8),(spades 7 , spades 8)

a) The probability of Emma having both 7s is $\frac{1}{5}=0.2$

b) The probability of having 7 of hearts is $\frac{3}{5}=0.6$