6 A box of biscuits contains 30 biscuits, some of which are wrapped in gold foil and some of which are unwrapped. Some of the biscuits are chocolate-covered. 12 biscuits are wrapped in gold foil, and of these biscuits, 7 are chocolate-covered. There are 17 chocolate-covered biscuits in total.
- Copy and complete the table below to show the number of biscuits in each category.
| Wrapped in gold foil | Unwrapped | Total |
| Chocolate-covered | | | |
| Not chocolate-covered | | | |
| Total | | | 30 |
A biscuit is selected at random from the box. - Find the probability that the biscuit is wrapped in gold foil.
The biscuit is returned to the box. An unwrapped biscuit is then selected at random from the box.
- Find the probability that the biscuit is chocolate-covered.
The biscuit is returned to the box. A biscuit is then selected at random from the box.
- Find the probability that the biscuit is unwrapped, given that it is chocolate-covered.
The biscuit is returned to the box. Nasir then takes 4 biscuits without replacement from the box.
- Find the probability that he takes exactly 2 wrapped biscuits.