A factory produces chocolates in three flavours: lemon, orange and strawberry in the ratio 3 : 5 : 7 respectively. Nell checks the chocolates on the production line by choosing chocolates randomly one at a time.
(a) Question
Find the probability that the first chocolate with lemon flavour that Nell chooses is the 7th chocolate that she checks.
Answer/Explanation
Ans:
\(\left [ Probability of lemon = \frac{3}{15} = \frac{1}{5}\right ]\)
\(\left [ \left ( \frac{4}{5} \right )^{6} \times \frac{1}{5}\right ]\frac{4096}{78125}, 0.0524\)
(b) Question
Find the probability that the first chocolate with lemon flavour that Nell chooses is after she has checked at least 6 chocolates.
‘Surprise’ boxes of chocolates each contain 15 chocolates: 3 are lemon, 5 are orange and 7 are strawberry.
Petra has a box of Surprise chocolates. She chooses 3 chocolates at random from the box. She eats each chocolate before choosing the next one.
Answer/Explanation
Ans:
\(\left ( 1-\frac{1}{5} \right )^{6}\)
\(\frac{4096}{15625}, 0.262\)
(c) Question
Find the probability that none of Petra’s 3 chocolates has orange flavour.
Answer/Explanation
Ans:
\(\frac{10}{15}\times \frac{9}{14}\times \frac{8}{13}\)
\(\frac{24}{91}, 0.264\)