Question

In the two upcoming basketball games, the probability that utc will defeat marshall is 0.63, and the probability that utc will defeat furman is 0.55. the probability that utc will defeat both opponents is 0.3465. what is the probability that utc will defeat furman given that they defeat marshall

Answer 1

Let $M$ denote the event that UTC beats Marshall, so that $\mathbb P(M)=0.63$, and let $F$ denote the event that UTC beats Furman, so that $\mathbb P(F)=0.55$. We're told that the UTC has a $\mathbb P(M\cap F)=0.3465$ probability of beating both Marshall and Furman.

So, by the definition of conditional probability, the probability of UTC beating Furman after having beaten Marshall is

$\mathbb P(F\mid M)=\dfrac{\mathbb P(F\cap M)}{\mathbb P(M)}=\dfrac{0.3465}{0.63}=0.55$