Exercise 18 Page 698

	Goalie	No Goalie
Redbirds Score	0.1	0.3
Bluebirds Score	0.1	0.6

Let's mark the event of the Redbirds scoring as R, the event of the Bluebirds scoring as B, and the event of leaving the goalie in as G. We are interested in the probability of two events R|G and B|G. Here B means the complement of event B, the Bluebirds not scoring. Let's start with using the formula for the probability of a complement to calculate P(B|G). P(B|G)=1-P(B|G)=1- 0.1= 0.9 Note that the events we are interested in are independent, since scoring by one team does not effect scoring by the other team. Recall the formula for the probability of two independent events. P(AandB)=P(A)* P(B) We can use this formula to calculate the desired probability. Let's do it!

P((R|G)and(B|G))=P(R|G) * P(B|G)

SubstituteII

P(R|G)= 0.1, P(B|G)= 0.9

P((R|G)and(B|G))= 0.1* 0.9

Multiply

Multiply

P((R|G)and(B|G))=0.09

WritePercent

Convert to percent

P((R|G)and(B|G))=9%

The probability that the Redbirds score and the Bluebirds do not score when the coach leaves the goalie in is 0.09, or 9%.