Two-way table of activities and age groups: a probability, a joint probability, a test for independence, a conditional probability and two members chosen together
Two-way table of activities and age groups: a probability, a joint probability, a test for independence, a conditional probability and two members chosen together
12 marks
The table below shows the main activity and the age group of each of the \(230\) members of a leisure centre.
| Under 30 | \(30\) and over | Total | |
|---|---|---|---|
| Swimming | \(55\) | \(15\) | \(70\) |
| Tennis | \(40\) | \(20\) | \(60\) |
| Yoga | \(45\) | \(55\) | \(100\) |
| Total | \(140\) | \(90\) | \(230\) |
- One member of the centre is chosen at random. Let \(A\) be the event that the member's main activity is yoga, and let \(B\) be the event that the member is aged \(30\) or over.[6]
- Find \(\mathrm{P}(A)\).
- Find the probability that the member does yoga and is aged \(30\) or over.
- Determine whether the events \(A\) and \(B\) are independent. Justify your answer.
- A member whose main activity is tennis is chosen at random. Find the probability that this member is under \(30\).[2]
- Two different members of the centre are chosen at random. Find the probability that one of them is under \(30\) and the other is aged \(30\) or over.[4]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a)(i) \(\dfrac{10}{23}\) (a)(ii) \(\dfrac{11}{46}\) (a)(iii) not independent, since \(\mathrm{P}(A\cap B)=\dfrac{11}{46}\ne\mathrm{P}(A)\,\mathrm{P}(B)=\dfrac{90}{529}\) (b) \(\dfrac23\) (c) \(0.478\)
Need help? Join our JC Math tuition classes.
Learn more