Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

The box holds $30$ biscuits altogether. Some biscuits are wrapped in gold foil and the rest are unwrapped, and some biscuits are chocolate-covered. Of the $12$ biscuits wrapped in gold foil, $7$ are chocolate-covered. In total, there are $17$ chocolate-covered biscuits.
(i)[2]

Copy and complete the table below to show how many biscuits are in each category.

(ii)[1]

A biscuit is chosen at random from the box. Find the probability that it is wrapped in gold foil.

(iii)[1]

The biscuit is put back into the box. An unwrapped biscuit is then chosen at random from the box. Find the probability that it is chocolate-covered.

(iv)[1]

The biscuit is put back into the box. A biscuit is then chosen at random from the box. Find the probability that it is unwrapped, given that it is chocolate-covered.

(v)[4]

The biscuit is put back into the box. Nasir then takes $4$ biscuits without replacement from the box. Find the probability that exactly $2$ of them are wrapped biscuits.

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