Tom Brady, the New England Patriots\' starting quarterback, was suspended for th
ID: 3336332 • Letter: T
Question
Tom Brady, the New England Patriots' starting quarterback, was suspended for the first 4 games of the regular season and could not play. The Patriots probability of winning is 60% without Brady playing and 83% with Brady playing. Assumptions: that each game is independent, and Brady plays in all 12 regular season games he is eligible to play in.
a) What is the probability that the Patriots win at least 15 regular season games?
b) Given that the Patriots won at least 15 regular season games, what is the probability that they lost 0 games in which Brady played?
Explanation / Answer
Total no of games = 16 (i.e 4+12)
a)
probability that the Patriots win at least 15 regular season games = probability that the Patriots win exactly 15 regular season games + probability that the Patriots win exactly 16 regular season games
probability that the Patriots win exactly 15 regular season games = probability that the Patriots lost in one game without Brady and won all other games + probability that the Patriots lost in one game with Brady and won all other games
= 4*(1-0.6)*0.603*0.8312 + 0.604*12*(1-0.83)*0.8311
= 0.070989
probability that the Patriots won all games
= 0.64*0.*8312 = 0.01385
probability that the Patriots win at least 15 regular season games = 0.070989 + 0.01385 = 0.084839
b)
probability that they lost 0 games in which Brady played given that Patriots won at least 15 regular season games
= (probability that they lost 0 games in which Brady played and Patriots won at least 15 regular season games)/probability that Patriots won at least 15 regular season games
probability that they lost 0 games in which Brady played and Patriots won at least 15 regular season games = probability that the Patriots lost in one game without Brady and won all other games + probability that the Patriots won all games
= 4*(1-0.6)*0.603*0.8312 +0.604*0.8312 = 0.050794
probability that they lost 0 games in which Brady played and Patriots won at least 15 regular season games = 0.050794/0.084839 = 0.59871
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.