In a 5

In a football game, Mike, gets to play be the goalkeeper 50% of the time if Peter is the coach. But if Robert is coaching, he only has 30% chance. Peter coaches more than Robert in about 6 to 10 games. What is the probability that Mike gets to be the goalie today?

Correct result:

p =  0.42

Solution:

$$\begin{gathered} P=6\mathrm{/}10={\displaystyle \frac{3}{5}}=0.6 \\ R=1-P=1-0.6={\displaystyle \frac{2}{5}}=0.4 \\ {p}_1=0.50\cdot P=0.50\cdot 0.6={\displaystyle \frac{3}{10}}=0.3 \\ {p}_2=0.30\cdot R=0.30\cdot 0.4={\displaystyle \frac{3}{25}}=0.12 \\ p=p_1+p_2=0.3+0.12={\displaystyle \frac{21}{50}}=0.42 \end{gathered}$$

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