Conditional probabilities from sports club membership counts and whether two activities are independent or mutually exclusive
Conditional probabilities from sports club membership counts and whether two activities are independent or mutually exclusive
6 marks
A sports club has \(136\) members. Of these, \(12\) members both swim and cycle, \(36\) swim but do not cycle, \(22\) cycle but do not swim, and the remaining \(66\) members do neither activity. One member of the club is chosen at random.
- Find the probability that the member cycles, given that the member swims.[2]
- Find the probability that the member cycles, given that the member does not swim.[2]
- Determine whether the events "the member swims" and "the member cycles" are mutually exclusive, independent or neither. Give a reason for your answer.[2]
Solution:
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Answer:(a) \(\dfrac14\) (b) \(\dfrac14\) (c) independent, since \(\mathrm{P}(C\mid S)=\mathrm{P}(C)=\dfrac14\); not mutually exclusive, since \(12\) members do both
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