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Tree diagram for two biscuits taken without replacement and the probability of one of each kind

Tree diagram for two biscuits taken without replacement and the probability of one of each kind

6 marks

A tin holds \(5\) chocolate biscuits \((C)\) and \(3\) ginger biscuits \((G)\). Lena takes a biscuit at random from the tin and eats it. She then takes a second biscuit at random from those left in the tin.

  1. Write the missing probabilities on the branches of the tree diagram below.[3]
______
\(C\)
______
\(G\)
______
\(C\)
______
\(G\)
______
\(C\)
______
\(G\)
  1. Find the probability that Lena eats one chocolate biscuit and one ginger biscuit.[3]

Solution:

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Answer:(a) first biscuit: \(C\) \(\dfrac58\), \(G\) \(\dfrac38\); after \(C\): \(C\) \(\dfrac47\), \(G\) \(\dfrac37\); after \(G\): \(C\) \(\dfrac57\), \(G\) \(\dfrac27\) (b) \(\dfrac{15}{28}\)

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