3 A particular brand of spread is produced in three varieties: standard, light and very light.
During a marketing campaign, the producer advertises that some cartons of spread contain coupons worth \(\pounds 1 , \pounds 2\) or \(\pounds 4\).
For each variety of spread, the proportion of cartons containing coupons of each value is shown in the table.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Variety |
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Standard | Light | Very light |
| No coupon | 0.70 | 0.65 | 0.55 |
| £1 coupon | 0.20 | 0.25 | 0.30 |
| £2 coupon | 0.08 | 0.06 | 0.10 |
| £4 coupon | 0.02 | 0.04 | 0.05 |
For example, the probability that a carton of standard spread contains a coupon worth \(\pounds 2\) is 0.08 .
In a large batch of cartons, 55 per cent contain standard spread, 30 per cent contain light spread and 15 per cent contain very light spread.
- A carton of spread is selected at random from the batch. Find the probability that the carton:
- contains standard spread and a coupon worth \(\pounds 1\);
- does not contain a coupon;
- contains light spread, given that it does not contain a coupon;
- contains very light spread, given that it contains a coupon.
- A random sample of 3 cartons is selected from the batch.
Given that all of these 3 cartons contain a coupon, find the probability that they each contain a different variety of spread.
[0pt]
[4 marks]