Question

Three cards are drawn off of a well shuffled standard deck of cards. What is the probability the first card is a 5 or 6 or spades?

Answer 1

answer is 0.3654

P(5)=4/52=1/13, P(6)=4/52=1/13, P(spade)=13/52=1/4

P(5 and 6)=0, P(5 and spade)=1/52, P(6 and spade)=1/52, P(5 and 6 and spade)=0

P(5 or 6 or spade)=P(5)+P(6)+P(spade)-P(5 and 6)-P(5 and spade)-P(6 and spade)+P(5 and 6 and spade)=

=4/52 + 4/52 + 13/52 - 0 - 1/52 - 1/52 + 0=19/52

required probability the first card is a 5 or 6 or spades=19/52=0.3654