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Completing a tree diagram for dependent events, a total probability and a reverse conditional probability

Completing a tree diagram for dependent events, a total probability and a reverse conditional probability

4 marks

At a restaurant, \(S\) is the event that a diner orders a starter and \(D\) is the event that the diner orders a dessert. The events are dependent, with \(\mathrm{P}(S)=0.35\), \(\mathrm{P}(D\mid S)=0.8\) and \(\mathrm{P}(D\mid S')=0.3\).

\(0.35\)
\(S\)
______
\(S'\)
______
\(D\)
______
\(D'\)
______
\(D\)
______
\(D'\)
Starter
Dessert
  1. Write the missing probabilities on the tree diagram.
  2. Find the probability that a diner orders a dessert.
  3. A diner orders a dessert. Find the probability that this diner also ordered a starter.

[4]

Solution:

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Answer:(a) \(S'\): \(0.65\); after \(S\): \(D\) \(0.8\), \(D'\) \(0.2\); after \(S'\): \(D\) \(0.3\), \(D'\) \(0.7\) (b) \(0.475\) (c) \(\dfrac{56}{95}\approx0.589\)

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