Box $$\(A\)$$ contains 7 red balls and 1 blue ball. Box $$\(B\)$$ contains 9 red balls and 5 blue balls. A ball is chosen at random from box $$\(A\)$$ and placed in box $$\(B\)$$. A ball is then chosen at random from box $$\(B\)$$. The tree diagram below shows the possibilities for the colours of the balls chosen. Find the probability that the ball chosen from box $$\(A\)$$ is blue given that the ball chosen from box $$\(B\)$$ is blue. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_52 Year：2020 Question No：6(c)
Answer:
\(\mathrm{P}(\mathrm{A}\) blue \(\mid \mathrm{B}\) blue \()=\frac{\mathrm{P}(\mathrm{A} \text { blue } \cap \mathrm{B} \text { blue })}{\mathrm{P}(\mathrm{B} \text { blue })}\)
\(=\frac{\frac{1}{8} \times \frac{6}{15}}{\frac{7}{8} \times \frac{5}{15}+\frac{1}{8} \times \frac{6}{15}}=\frac{\frac{1}{20}}{\frac{41}{120}}\)
\(=\frac{6}{41}\) or \(0.146\)
\(=\frac{\frac{1}{8} \times \frac{6}{15}}{\frac{7}{8} \times \frac{5}{15}+\frac{1}{8} \times \frac{6}{15}}=\frac{\frac{1}{20}}{\frac{41}{120}}\)
\(=\frac{6}{41}\) or \(0.146\)
Knowledge points:
5.3.4 calculate and use conditional probabilities in simple cases.
Solution:
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