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4.4 Probability (A-level only)

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Question 82

A club manager surveyed 30 members about their use of the gym and the swimming pool.

He finds that, of the 30 members:

  • 18 use the gym
  • 10 use the swimming pool
  • 6 use both the gym and the swimming pool
a.

A member is chosen at random from the 30 surveyed. Determine whether the event 'the member uses the gym' and the event 'the member uses the swimming pool' are independent.

[3]
b.

For the entire health club, it is known that:

  • the probability that a member uses the sauna is P(S)=14P(S) = \frac{1}{4}P(S)=41​
  • the probability that a member uses the steam room is P(T)=13P(T) = \frac{1}{3}P(T)=31​
  • the probability that a member uses the steam room given that they use the sauna is P(T∣S)=25P(T|S) = \frac{2}{5}P(T∣S)=52​

Calculate the probability that a member uses the sauna or the steam room or both.

[3]

4.4 Probability (A-level only) Questions

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