Solution-
The table shows the number of touchdowns Luis scored during his football games.
Touchdowns scored (X) 0 1 2 3
Number of games (f) 6 10 7 5
Total games played = 6+10+7+5=28
1.
[tex]Probability\ of\ an\ event=\frac{Number\ of\ Favorable\ Outcomes}{Total\ Number\ of\ Possible\ Outcomes}[/tex]
[tex]P(X=0)=\frac{6}{28} \\ P(X=1)=\frac{10}{28} \\ P(X=2)=\frac{7}{28} \\ P(X=3)=\frac{5}{28}[/tex]
Probability Distribution Table,
Touchdowns scored (X) 0 1 2 3
Probability P(X) 6/28 10/28 7/28 5/28
2.
The probability of Luis scoring 2 touchdowns(i.e when X=2),
P(scoring 2 touchdowns) = P(X=2)
[tex]=\frac{7}{28}=0.25[/tex]
3.
The probability of Luis scoring more than 1 touchdown(i.e when X>1)
P(scoring more than 1 touchdowns) = P(X>1) = P(X=2) + P(X=3)
[tex]=\frac{7}{28}+\frac{5}{28}=0.42[/tex]
4.
Estimated number of touchdowns is calculated by multiplying the number of touchdowns by their respective probabilities and adding the result.
Estimated number of touchdowns is,
[tex]=0\times \frac{6}{28}+1\times \frac{10}{28}+2\times \frac{7}{28}+3\times \frac{5}{28}[/tex]
[tex]=0+\frac{10}{28}+\frac{14}{28}+\frac{15}{28}[/tex]
[tex]=\frac{39}{28}=1.39[/tex]
