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WAEC Mathematics 2016 Paper

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Question : 41

Total: 49

A bag contains 5 red and 4 blue identical balls. Id two balls are selected at random from the bag, one after the other, with replacement, find the probability that the first is red and the second is blue

$\;\frac{2}{9}$
$\;\frac{5}{18}$
$\;\frac{20}{81}$
$\;\frac{5}{9}$

Solution:

Concept:

With replacement means the total number of balls stays the same for both draws.

Explanation:

Total balls

= 5 + 4 = 9

.

Probability that the first ball is red

= \frac{5}{9}

.

Since the ball is replaced, the second draw still has 9 balls.

Probability that the second ball is blue

= \frac{4}{9}

.

These events are independent, so multiply the probabilities.

P(\text{red then blue}) = \frac{5}{9} \times \frac{4}{9}

= \frac{20}{81}

.

Answer:

\frac{20}{81}

Correct option: C.

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