# Probability, but dealing with percentages as opposed to numbers of people?

In a class of Distance Education Students studying Management Science in which all students play at least one sport, 60% of these students play cricket or rugby and 10% play both sports. If there is also 60% that do not play cricket, calculate the probability that a student chosen at random from the class:

(i) Plays cricket only: 30%

(ii) Plays rugby only: 20%

(iii) Plays only one of the sports, cricket and rugby: 50%

(iv) Plays neither cricket or rugby: 40%

• I would start by drafting a Venn-diagram. It will make it much easier to visualize the different cases. – Matti P. Nov 8 at 10:25
• Thanks I'll try that – Michael O' Driscoll Nov 8 at 10:26
• @MattiP. please check my reasoning – Michael O' Driscoll Nov 8 at 10:34
• Small mistake: The problem statement says " there is also $60~\%$ who don't play cricket -- meaning that the number of cricket players (that is, those who only play cricket, union with those who play cricket and rugby) is 40 per cent. You can also infer that this means that the number of people who play only cricket is 30 per cent. – Matti P. Nov 8 at 10:44
• I'll reedit my answer thanks – Michael O' Driscoll Nov 8 at 10:46