A-LevelMathematicsProbability and statistics9709/63 · May/June 2019 · Q26 Marks

Megan sends messages to her friends in one of 3 different ways: text, email or social media. For each message, the probability that she uses text is 0.3 and the probability that she uses email is 0.2. She receives an immediate reply from a text message with probability 0.4, from an email with probability 0.15 and from social media with probability 0.6.

(i)Draw a fully labelled tree diagram to represent this information.[2]
(ii)Given that Megan does not receive an immediate reply to a message, find the probability that the message was an email.[4]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] Fully correct labelled tree with correct probabilities for 'Send'
[B1] Fully correct labelled branches with correct probabilities for the 'reply'
[M1] P(email) × P(NR) seen as numerator of a fraction, consistent with their tree diagram
[M1] Summing three appropriate 2-factor probabilities, consistent with their tree diagram, seen anywhere
0.55 oe (can be unsimplified) seen as denom of a fraction
[A1] Correct answer

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