SPM.1.SL.TZ0.13

pestleMathematicsAISLPaper 1SPM· sl-4-5-probability-concepts-expected-numberssource ↗

Mr Burke teaches a mathematics class with 15 students. In this class there are 6 female students and 9 male students.

Each day Mr Burke randomly chooses one student to answer a homework question.

In the first month, Mr Burke will teach his class 20 times.

Find the probability that on any given day Mr Burke chooses a female student to answer a question.

[1]

Find the probability he will choose a female student 8 times.

[2]

Find the probability he will choose a male student at most 9 times.

[3]

Markscheme / solution

$\frac{6}{{15}}\left( {0.4,\,\frac{2}{5}} \right)$ A1

[1 mark]

P(X = 8) (M1)

Note: Award (M1) for evidence of recognizing binomial probability. eg P(X = 8), X ∼ B $\left( {20,\,\frac{6}{{15}}} \right)$ .

0.180 (0.179705…) A1

[2 marks]

P(male) = $\frac{9}{{15}}\left( {0.6} \right)$ A1

P(X ≤ 9) = 0.128 (0.127521…) (M1)A1

Note: Award (M1) for evidence of correct approach eg, P(X ≤ 9).

[3 marks]

Examiners’ report

[N/A]