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Missing branch probability on a two-stage tree diagram, a total probability and a reverse conditional probability

Missing branch probability on a two-stage tree diagram, a total probability and a reverse conditional probability

7 marks

The tree diagram below gives probabilities for two events, \(A\) and \(B\). The probability that \(A\) does not occur is \(p\).

\(\frac{1}{5}\)
\(A\)
\(p\)
\(A'\)
\(\frac{1}{4}\)
\(B\)
\(\frac{3}{4}\)
\(B'\)
\(\frac{3}{8}\)
\(B\)
\(\frac{5}{8}\)
\(B'\)
  1. Write down the value of \(p\).[1]
  2. Find \(P(B)\).[3]
  3. Find \(P(A'\mid B)\).[3]

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Answer:(a) \(\frac{4}{5}\) (b) \(\frac{7}{20}\) (c) \(\frac{6}{7}\)

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