Use expectation and binomial probabilities for repeated bus choices.
Use expectation and binomial probabilities for repeated bus choices.
7 marks
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Paula goes to work three days a week. On any day, the probability that she goes on a red bus is \(\frac14\).
Write down the expected number of times that Paula goes to work on a red bus in one week. In one week, find the probability that she goes to work on a red bus[2]
on exactly two days;[2]
on at least one day.[3]
Solution:
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Answer:\(P(X=2)=\binom32(\frac14)^2(\frac34)=\frac9{64}\), and \(P(X\ge1)=1-(\frac34)^3=\frac{37}{64}\).