Union and conditional probabilities from a two-way table of orchestra members, then two members chosen without replacement
Union and conditional probabilities from a two-way table of orchestra members, then two members chosen without replacement
7 marks
A youth orchestra has \(30\) members. Each member plays in exactly one section. The table shows the members by section and by age group.
| Strings | Woodwind | Brass | |
|---|---|---|---|
| Junior | \(6\) | \(5\) | \(3\) |
| Senior | \(9\) | \(4\) | \(3\) |
- One member is chosen at random.
- Find the probability that the member is a senior or plays woodwind.
- The member chosen is a junior. Find the probability that this member does not play strings.[4]
- Two different members are chosen at random. Find the probability that neither of them plays strings.[3]
Solution:
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Answer:(a)(i) \(\dfrac{7}{10}\) (a)(ii) \(\dfrac{4}{7}\) (b) \(\dfrac{7}{29}\)
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