Three coins $$\(A, B\)$$ and $$\(C\)$$ are each thrown once. - Coins $$\(A\)$$ and $$\(B\)$$ are each biased so that the probability of obtaining a head is $$\(\frac{2}{3}\)$$. - Coin $$\(C\)$$ is biased so that the probability of obtaining a head is $$\(\frac{4}{5}\)$$. Show that the probability of obtaining exactly 2 heads and 1 tail is $$\(\frac{4}{9}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_w20_qp_53 Year：2020 Question No：6(a)
Answer:
Scenarios:
\( \begin{array}{l}
\text { HHT: } \quad \frac{2}{3} \times \frac{2}{3} \times \frac{1}{5}=\frac{4}{45} \\ \text { HTH: } \quad \frac{2}{3} \times \frac{1}{3} \times \frac{4}{5}=\frac{8}{45} \\ \text { THH: } \quad \frac{1}{3} \times \frac{2}{3} \times \frac{4}{5}=\frac{8}{45} \\ \text { Total }=\frac{20}{45}=\frac{4}{9}
\end{array} \)
\( \begin{array}{l}
\text { HHT: } \quad \frac{2}{3} \times \frac{2}{3} \times \frac{1}{5}=\frac{4}{45} \\ \text { HTH: } \quad \frac{2}{3} \times \frac{1}{3} \times \frac{4}{5}=\frac{8}{45} \\ \text { THH: } \quad \frac{1}{3} \times \frac{2}{3} \times \frac{4}{5}=\frac{8}{45} \\ \text { Total }=\frac{20}{45}=\frac{4}{9}
\end{array} \)
Knowledge points:
5.3.1 evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events, or by calculation using permutations or combinations (e.g. the total score when two fair dice are thrown.) (e.g. drawing balls at random from a bag containing balls of different colours.)
5.3.2 use addition and multiplication of probabilities, as appropriate, in simple cases (Explicit use of the general formula is not required.)
Solution:
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