# Exam-Style Question on Probability

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 707. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is not allowed.

On a Tuesday at a theme park, a sample of 50 visitors was randomly selected as they were leaving the park. They were asked how many times that day they had been on a ride called The Serpent. This information is summarised in the following frequency table.

Number of times on The Serpent Frequency
0 6
1 12
2 17
3 10
4 5

It can be assumed that this sample is representative of all visitors to the park for the following day.

(a) For the following day, Wednesday, estimate

(i) the probability that a randomly selected visitor will ride The Serpent;

(ii) the expected number of times a visitor will ride The Serpent.

It is known that 2000 visitors will attend the amusement park on Wednesday. The Serpent can carry a maximum of 18 people each time it runs.

(b) Estimate the minimum number of times The Serpent must run to satisfy demand.

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