17N.1.SL.TZ0.S_1

pestleMathematicsAISLPaper 117N· sl-4-5-probability-concepts-expected-numberssource ↗

A bag contains 5 green balls and 3 white balls. Two balls are selected at random without replacement.

Complete the following tree diagram.

N17/5/MATME/SP1/ENG/TZ0/01.a

[3]

Find the probability that exactly one of the selected balls is green.

[3]

Markscheme / solution

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

correct probabilities

N17/5/MATME/SP1/ENG/TZ0/01.a/M A1A1A1 N3

Note: Award A1 for each correct bold answer.

[3 marks]

multiplying along branches (M1)

eg $\,\,\,\,\,$ $\frac{5}{8} \times \frac{3}{7},{\text{ }}\frac{3}{8} \times \frac{5}{7},{\text{ }}\frac{{15}}{{56}}$

adding probabilities of correct mutually exclusive paths (A1)

eg $\,\,\,\,\,$ $\frac{5}{8} \times \frac{3}{7} + \frac{3}{8} \times \frac{5}{7},{\text{ }}\frac{{15}}{{56}} + \frac{{15}}{{56}}$

$\frac{{30}}{{56}}{\text{ }}\left( { = \frac{{15}}{{28}}} \right)$ A1 N2

[3 marks]

Examiners’ report

[N/A]