Answer to Question #144855 in Statistics and Probability for rwan alqmash

Question

The CIC Basketball team ,play 40 percent of their games at night and 60 percent during the day .the team wins 50 percent of their night games and 80 percent of their day games.If they win What is the probability the game is played at night, If they lose What is the probability the game is played at nigh ,solve by using Bayes’ Theorem?

Answer 1

Lets denote d for playing day games, n for playing night games, w for winning the game and l for losing.

Then we have that:

$P(d) = 0.6$

$P(n) = 0.4$

$P(w|d) = 0.8$

$P(w|n) = 0.5$

If they win the probability the game is played at night:

$P(n|w)=\frac{P(w|n)P(n)}{P(w|n)P(n)+P(w|d)P(d)}=\frac{0.5\cdot0.4}{0.5\cdot0.4+0.8\cdot0.6}=0.294$

If they lose the probability the game is played at nigh:

$P(n|l)=\frac{P(l|n)P(n)}{P(l|n)P(n)+P(l|d)P(d)}$

where $P(l|n)=1-P(w|n)=1-0.5=0.5$

and $P(l|d)=1-P(w|d)=1-0.8=0.2$

$P(n|l)=\frac{0.5\cdot0.4}{0.5\cdot0.4+0.2\cdot0.6}=0.625$