Goalkeeper

Mike plays as the goalkeeper 50% of the time if Peter is the coach in a football game. However, if Robert were coaching, he would only have a 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 answer:

p =  0.42

Step-by-step explanation:

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

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