There are 8 chocolates in a box - HSC - SSCE Mathematics Standard - Question 11 - 2021 - Paper 1
Question 11
There are 8 chocolates in a box. Three have peppermint centres (P) and five have caramel centres (C).
Kim randomly chooses a chocolate from the box and eats it. Sam... show full transcript
Worked Solution & Example Answer:There are 8 chocolates in a box - HSC - SSCE Mathematics Standard - Question 11 - 2021 - Paper 1
Step 1
Kim chooses P, Sam chooses C
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Answer
The probability that Kim chooses a peppermint chocolate is ( P(K = P) = \frac{3}{8} ). After Kim has taken a peppermint chocolate, there are now 7 chocolates left, with 5 being caramel. Thus, the probability that Sam chooses a caramel chocolate is ( P(S = C | K = P) = \frac{5}{7} ). Therefore, the combined probability is:
P(K=P,S=C)=P(K=P)×P(S=C∣K=P)=83×75=5615.
Step 2
Kim chooses C, Sam chooses P
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Answer
The probability that Kim chooses a caramel chocolate is ( P(K = C) = \frac{5}{8} ). If Kim has taken a caramel chocolate, there are now 7 chocolates left: 3 being peppermint. Thus, the probability that Sam chooses a peppermint chocolate is ( P(S = P | K = C) = \frac{3}{7} ). Therefore, the combined probability is:
P(K=C,S=P)=P(K=C)×P(S=P∣K=C)=85×73=5615.
Step 3
Total probability of different centres
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Answer
The total probability that Kim and Sam choose chocolates with different centres is the sum of the two probabilities computed:
