Dunman High Prelims 2008 P1 Q9
A small box containing chocolates of which 3 contains hazelnuts, 7 contains almonds and 2 contain sultanas. Two chocolates are picked at random, one at a time, without replacement. Find the probability that
(a) both contain hazelnuts,
(b) one contains almonds and one contains hazelnuts,
(c) both are without sultanas.
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Answer:
(a) Probability that both contain hazelnuts
= probability of first chocolate containing hazelnuts and probability of second chocolate containing hazelnuts
= 3/12 * 2/11
= 1/22
(b) Probability that one contains almonds and one contains hazelnuts
= probability of first chocolate containing almonds and probability of second chocolate containing hazelnuts OR probability of first chocolate containing hazelnuts and probability of second chocolate containing almonds
= 7/12 * 3/11 + 3/12 * 7/11
= 7/44 + 7/44
= 7/22
(c) Probability that both are without sultanas
= probability of first chocolate NOT containing sultanas and probability of second chocolate NOT containing sultanas
= 10/12 * 9/11
= 15/22
