# Exam-Style Question on Binomial Distribution

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

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Question id: 322. This question is similar to one that appeared on an IB Standard paper in 2008. The use of a calculator is allowed.

Mr Willis goes to school (he's a Maths teacher) five times each week during term time. On any given day, the probability that he goes on an orange bus is $$\frac13$$.

(a) Write down the expected number of times that Mr Willis goes to work at his school on an orange bus in one week.

In one week, find the probability that he goes to work on an orange bus

(b) on exactly three days;

(c) on at least two days.

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If you are using a TI-nSpire CX calculator and you would like to see an example of the process used in this question see GDC Essentials.

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