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2.3 Probability

2.3 Probability

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Question 88

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]
Markscheme

2.3 Probability Questions

  1. A Level
  2. /Maths
  3. /2.3 Probability

200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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