Mathematics 9709 · AS & A Level · Probability

Probability — practice question

A factory makes chocolates in three flavours, lemon, orange and strawberry, in the ratio $3:5:7$ respectively. Nell checks the chocolates on the production line by selecting them at random one at a time.
(a)[1]

Find the probability that the first chocolate with lemon flavour that Nell chooses is the $7\text{th}$ chocolate that she checks.

(b)[2]

Find the probability that the first chocolate with lemon flavour that Nell chooses is after she has checked at least $6$ chocolates.

(c)[2]

'Surprise' boxes of chocolates each have $15$ chocolates: $3$ lemon, $5$ orange and $7$ strawberry. Petra has a box of Surprise chocolates. She takes $3$ chocolates at random from the box. She eats each chocolate before taking the next one. Find the probability that none of Petra’s $3$ chocolates has orange flavour.

(d)[3]

Find the probability that each of Petra’s $3$ chocolates has a different flavour.

(e)[4]

Find the probability that at least $2$ of Petra’s $3$ chocolates have strawberry flavour given that none of them has orange flavour.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct calculation of the probability for a lemon result

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