Question

The Beardstown Bearcats baseball team plays 60 percent of its games at night and 40 percent in the daytime. It wins 55 percent of its night games but only 35 percent of its day games. You read in the paper that the Bearcats won their last game against the Manteno Maulers. What is the probability that it was played at night?

Answer 1

Answer: 0.7021

Explanation:

Let D be the event that team plays in day , N be the event that the team plays in night and W be the event when team wins.

Then ,
`P(D)=0.40\ \ \ P(N)=0.60`

`P(W|D})=0.35\ \ \ \ P(W|N)=0.55`

Using the law of total probability , we have

`P(W)=P(D)*P(W|D)+P(N)*P(W|N)\\\\\Rightarrow\ P(W)=0.40*0.35+0.60*0.55=0.47`

Using Bayes theorem ,

The required probability :
`P(N|W)=(P(N)P(W|N))/(P(W))`

`=(0.60*0.55)/(0.47)=0.702127659574\approx0.7021`