In a certain village sports club, 46 % of members play football, 36 % of members play cricket, and 17 % of members play both games. What is the probability (between 0 and 1) that a randomly chosen member does not play football given that he/she plays cricket?
Give your solution accurate to 4 decimal places.
Let $F$ be the event that the person plays football and $C$ be the event they play cricket. Then, what you want is $$ P(F^c | C) = \frac{P(F^c \cap C)}{P(C)}. $$ Now, $P(F^c \cap C) = P(\text{the person plays cricket, but not football})$, which you can calculate, since you know that 17% play both cricket and football.