Honors: 9.03 Conditional probability

A basketball team has a probability of $0.8$0.8 of winning its first season and $0.15$0.15 of winning its first season and its second season. What is the probability of winning the second season, given they won first?

For events $A$A and $B$B we can find the probability of $A$A given $B$B using$P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$P(A|B)=P(A∩B)P(B)​.

The following are probabilities for an experiment in which $A$A and $B$B are two possible events.

$P\left(A\cap B\right)=0.48$P(A∩B)=0.48, and

$P\left(A\right)=0.6$P(A)=0.6.

Find $P\left(B|A\right)$P(B|A).