More about probability  (15.415.5)
Recognise the concept and notation of conditional probability

Theory

ExamplesIt is found that in a set of 2 free throws of a basketball player, the performance
in the second shot is affected by the first shot.
The probability for him to have the first successful free throw is 0.86, while the
probability for him to have both successful free throws is 0.52.
Find the probability for him to have the second successful free throw, given that he
has the first successful free throw. 
SolutionsLet A be the event that the player has the first successful free throw,
B be the event that the player has the second successful free throw.
\(\because \begin{array}{1}P(A) = 0.86\\P(A \cap B) = {0.52^{}}\end{array}\)
\( \begin{array}{1}\therefore \qquad P(BA) = & \,\frac{{P(A \cap B)}}{{P(A)}}\\ = & \,\frac{{0.52}}{{0.86}}\\ = & \,{\underline{\underline {\frac{{26}}{{43}}}} ^{}}\end{array}\)