Chapter 11.4, Problem 18PPSE

Solution

To identify:The probability that the team will win. A football team has a 70% chance of winning when it doesn't snow, but only a 40% chance of winning when it snows. Suppose there is a 50% chance of snow.

Theprobability that the team will win is $0.55$

Given information:

Team has a 70% chance of winning when it doesn't snow, but only a 40% chance of winning when it snows.

Explanation:

Consider the given information.

Let Wshows the event that the football team win the match and NW shows the event that the football team will not win the match And let S shows the event that it does snow and NS shows the event that it does not snow. There is a 50% chance of snow. So $P\left(S\right)=0.50$ and $P\left(NS\right)\text{ =}0.50$ So first branches of the tree diagrams will be

When it does not snow there is only 70% chance of winning so $P\left(W/NS\right)=0.70$ and when it snows there is only 40% chance of winning so $P\left(W/S\right)=0.40$ Therefore the tree diagram will be

Probability of winning the team will be

  $\begin{array}{c}P\left(W\right)=P\left(WandS\right)+P\left(WandNS\right)\\ =0.50\cdot 0.40+0.50\cdot 0.70\\ =0.20+0.35\\ =0.55\end{array}$

So, the probability that the team will win is $0.55$