what is the probability (between 0 and 1)?

Question

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.

Answer 1

Let's suppose that the membership is N, then we can convert the prevents into actual numbers.

We can represent the sets by three circles. A large circle represents the membership of N. Inside there are two interlocking circles, representing cricket and football players. Where they overlap there are 0.17N members who play both games. That means that (0.46-0.17)N=0.29N only play football and (0.36-0.17)N=0.19N only play cricket. The total number that play one or both games=(0.29+0.19+0.17)N=0.65N, so (1-0.65)N=0.35N play neither game. The probability of a random player being a cricket player but not a football player is 0.19N/N=0.19 or 0.1900.