The table shows the favourite drink of \(200\) people. Drink Tea Coffee Juice Water Number of people 62 78 35 25 (a) One of these people is chosen at random...
Question 1 Report
The table shows the favourite drink of \(200\) people.
| Drink | Tea | Coffee | Juice | Water |
|---|---|---|---|---|
| Number of people | 62 | 78 | 35 | 25 |
(a) One of these people is chosen at random. Write down the probability that juice is their favourite drink. [1]
(b) Write down the probability that tea or water is their favourite drink. [1]
(c) A different group of \(500\) people is surveyed. Estimate the number of these people whose favourite drink is coffee. [2]
Answer Details
(a) The frequencies in the table total \(200\), which matches the number of people surveyed, so a probability is a frequency divided by \(200\).
\[ P(\text{juice}) = \frac{35}{200} = \frac{7}{40} \] [B1]
(b) Tea and water are mutually exclusive, since each person names only one favourite, so their frequencies add.
\[ P(\text{tea or water}) = \frac{62 + 25}{200} = \frac{87}{200} \] [B1]
(c) The proportion choosing coffee in the survey is used as an estimate of the proportion in the new group, then applied to \(500\) people.
\[ \frac{78}{200} \times 500 \] [M1]
\[ = 0.39 \times 500 = 195 \text{ people} \] [A1]
Equivalent forms such as \(0.175\) in (a) and \(0.435\) in (b) are accepted. Part (c) is an estimate: it assumes the second group has similar tastes to the first, which is exactly the assumption that makes a sample useful for prediction.
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