The table shows the colour of the pen 200 people took during a game.

  1. (a)

    A person is selected at random. Find, as a percentage, the probability that the person took a black pen.

  2. (b)

    Two persons are selected at random. Find the probability, as a fraction in its lowest terms, that both of them are girls who took red pens.

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Worked solution

20(a)

1. Find the total number of people who took a black pen.

Number who took black pens
=15+23=38=15+23=38

2. Convert the probability into a percentage.

Total number of people =200=200.

Probability as a percentage
=38200×100%=19%=\frac{38}{200}\times 100\%=19\%

Answer

19%19\%

20(b)

1. Identify the number of girls who took red pens and set up the probability for two selections without replacement.

From the table, the number of girls who took red pens is 55.

Since two persons are selected at random without replacement,
P(both are girls who took red pens)=5200×4199.P(\text{both are girls who took red pens})=\frac{5}{200}\times\frac{4}{199}.

2. Calculate and simplify the probability to lowest terms.

5200×4199=2039800=11990.\frac{5}{200}\times\frac{4}{199}=\frac{20}{39800}=\frac{1}{1990}.

Correction: since 200×199=39800200 \times 199 = 39800, and 5×4=205 \times 4 = 20,
2039800=11990.\frac{20}{39800}=\frac{1}{1990}.

Answer

11580\dfrac{1}{1580}

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