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WAEC Mathematics 2019 Paper

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Question : 33

Total: 50

A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?

$\frac{2}{3}$
$\frac{3}{5}$
$\frac{7}{20}$
$\frac{12}{25}$

Solution:

Concept:

Probability of different colours when drawing two balls with replacement.

Explanation:

Total balls

= 2 + 3 = 5

.

P(white)

= \frac{2}{5}

and P(blue)

= \frac{3}{5}

.

Since replacement occurs, the probabilities remain the same for the second draw.

Different colours can happen in two orders: white then blue, or blue then white.

Required probability

= \left(\frac{2}{5} \times \frac{3}{5}\right) + \left(\frac{3}{5} \times \frac{2}{5}\right)

.

= \frac{6}{25} + \frac{6}{25} = \frac{12}{25}

.

Answer:

\frac{12}{25}

Option D.

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