20N.1.SL.TZ0.T_14

pestleMathematicsAASLPaper 120N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

Andre will play in the semi-final of a tennis tournament.

If Andre wins the semi-final he will progress to the final. If Andre loses the semi-final, he will not progress to the final.

If Andre wins the final, he will be the champion.

The probability that Andre will win the semi-final is $p$ . If Andre wins the semi-final, then the probability he will be the champion is $0.6$ .

The probability that Andre will not be the champion is $0.58$ .

Complete the values in the tree diagram.

[1]

Find the value of $p$ .

[2]

Given that Andre did not become the champion, find the probability that he lost in the semi-final.

[3]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

(A1) (C1)

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

[1 mark]

$p \times 0.4 + (1 - p) = 0.58$ (M1)

Note: Award (M1) for multiplying and adding correct probabilities for losing equated to $0.58$ .

OR

$p \times 0.6 = 1 - 0.58$ (M1)

Note: Award (M1) for multiplying correct probabilities for winning equated to $1 - 0.58$ or $0.42$ .

$(p =) 0.7$ (A1)(ft) (C2)

Note: Follow through from their part (a). Award the final (A1)(ft) only if their $p$ is within the range $0 < p < 1$ .

[2 marks]

$\frac{0.3}{0.58} (\frac{1 - 0.7}{0.58})$ (A1)(ft)(A1)

Note: Award (A1)(ft) for their correct numerator. Follow through from part (b). Award (A1) for the correct denominator.

OR

$\frac{0.3}{0.3 + 0.7 \times 0.4}$ (A1)(ft)(A1)(ft)

Note: Award (A1)(ft) for their correct numerator. Follow through from part (b). Award (A1)(ft) for their correct calculation of Andre losing the semi-final or winning the semi-final and then losing in the final. Follow through from their parts (a) and (b).

$\frac{15}{29} (0.517, 0.517241 \dots, 51.7 %)$ (A1)(ft) (C3)

Note: Follow through from parts (a) and (b).

[3 marks]

Examiners’ report

[N/A]