A legendary football coach was known for his winning seasons. He consistently won nine or more games perseason. Suppose x equals the number of games won up to the halfway mark (six games) in a 12-game season. Ifthis coach and his team had a probability p = 0.75 of winning any one game (and the winning or losing of onegame was independent of another), then the probability distribution of the number x of winning games in aseries of six games is: $$\begin{array} { l | l }
x & P ( x ) \
\hline 0 & 0.000244 \
1 & 0.004395 \
2 & 0.032959 \
3 & 0.131836 \
4 & 0.296631 \
5 & 0.355957 \
6 & 0.177979
\end{array}$$ Find the expected number of winning games in the first half of the season for this coachʹs football teams.

Question

A legendary football coach was known for his winning seasons. He consistently won nine or more games perseason. Suppose x equals the number of games won up to the halfway mark (six games) in a 12-game season. Ifthis coach and his team had a probability p = 0.75 of winning any one game (and the winning or losing of onegame was independent of another), then the probability distribution of the number x of winning games in aseries of six games is: $$\begin{array} { l | l } 
x & P ( x ) \
\hline 0 & 0.000244 \
1 & 0.004395 \
2 & 0.032959 \
3 & 0.131836 \
4 & 0.296631 \
5 & 0.355957 \
6 & 0.177979
\end{array}$$ Find the expected number of winning games in the first half of the season for this coachʹs football teams.

Quizplus · Accepted Answer

The Answer of A legendary football coach was known for his winning seasons. He consistently won nine or more games perseason. Suppose x equals the number of games won up to the halfway mark (six games) in a 12-game season. Ifthis coach and his team had a probability p = 0.75 of winning any one game (and the winning or losing of onegame was independent of another), then the probability distribution of the number x of winning games in aseries of six games is: $$\begin{array} { l | l } 
x & P ( x ) \
\hline 0 & 0.000244 \
1 & 0.004395 \
2 & 0.032959 \
3 & 0.131836 \
4 & 0.296631 \
5 & 0.355957 \
6 & 0.177979
\end{array}$$ Find the expected number of winning games in the first half of the season for this coachʹs football teams.

A Legendary Football Coach Was Known for His Winning Seasons