Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

It was discovered that $68\%$ of the passengers on a train used a cell phone during the journey. Among those who used a cell phone, $70\%$ were younger than $30$ years, $25\%$ were aged between $30$ and $65$ years and the remainder were over $65$ years old. Among the passengers who did not use a cell phone, $26\%$ were under $30$ years old and $64\%$ were over $65$ years old, while the rest were between $30$ and $65$ years old.
(a)[2]

Draw a tree diagram to show this information, and write every probability as a decimal.

(b)[3]

If one passenger is known to be $45$ years old, find the probability that this passenger used a cell phone during the journey.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Probability tree begins with the correct first split, showing $P(H)$ and $P(\overline{H})$

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