16N.1.SL.TZ0.T_12

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On a work day, the probability that Mr Van Winkel wakes up early is $\frac{4}{5}$ .

If he wakes up early, the probability that he is on time for work is $p$ .

If he wakes up late, the probability that he is on time for work is $\frac{1}{4}$ .

The probability that Mr Van Winkel arrives on time for work is $\frac{3}{5}$ .

Complete the tree diagram below.

N16/5/MATSD/SP1/ENG/TZ0/12.a

[2]

Find the value of $p$ .

[4]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

N16/5/MATSD/SP1/ENG/TZ0/12.a/M (A1)(A1) (C2)

Note: Award (A1) for each correct pair of probabilities.

[2 marks]

$\frac{4}{5}p + \frac{1}{5} \times \frac{1}{4} = \frac{3}{5}$ (A1)(ft)(M1)(M1)

Note: Award (A1)(ft) for two correct products from part (a), (M1) for adding their products, (M1) for equating the sum of any two probabilities to $\frac{3}{5}$ .

$(p = ){\text{ }}\frac{{11}}{{16}}{\text{ }}(0.688,{\text{ }}0.6875)$ (A1)(ft) (C4)

Note: Award the final (A1)(ft) only if $0 \leqslant p \leqslant 1$ . Follow through from part (a).

[4 marks]

Examiners’ report

[N/A]