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Date May 2008 Marks available 3 Reference code 08M.1.sl.TZ2.6
Level SL only Paper 1 Time zone TZ2
Command term Calculate Question number 6 Adapted from N/A

Question

There are 20 students in a classroom. Each student plays only one sport. The table below gives their sport and gender.


One student is selected at random.

(i)     Calculate the probability that the student is a male or is a tennis player.

(ii)    Given that the student selected is female, calculate the probability that the student does not play football.

[4]
a(i) and (ii).

Two students are selected at random. Calculate the probability that neither student plays football.

[3]
b.

Markscheme

(i) correct calculation     (A1)

e.g. \(\frac{9}{{20}} + \frac{5}{{20}} - \frac{2}{{20}}\) , \(\frac{{4 + 2 + 3 + 3}}{{20}}\)

\({\text{P(male or tennis)}} = \frac{{12}}{{20}}\)     A1     N2

(ii) correct calculation     (A1)

e.g. \(\frac{6}{{20}} \div \frac{{11}}{{20}}\) , \(\frac{{3 + 3}}{{11}}\)

\({\text{P(not football|female)}} = \frac{6}{{11}}\)     A1     N2

[4 marks]

a(i) and (ii).

\({\text{P(first not football)}} = \frac{{11}}{{20}}\) , \({\text{P(second not football)}} = \frac{{10}}{{19}}\)     A1

\({\text{P(neither football)}} = \frac{{11}}{{20}} \times \frac{{10}}{{19}}\)     A1

\({\text{P(neither football)}} = \frac{{110}}{{380}}\)     A1     N1

[3 marks]

b.

Examiners report

Many candidates had difficulty with this question, usually as a result of seeking to solve the problem by formula instead of looking carefully at the table frequencies.

a(i) and (ii).

A very common error in part (b) was to assume identical probabilities for each selection instead of dependent probabilities where there is no replacement.

b.

Syllabus sections

Topic 5 - Statistics and probability » 5.6 » Probabilities with and without replacement.

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