A bag contains 4 white marbles and 3 red marbles. Another bag contains 5 red...

WAEC 2023

A bag contains 4 white marbles and 3 red marbles. Another bag contains 5 red and 6 blue marbles. If a marble is picked at random from each bag, find the probability that they are of the same colour.

A. \(\frac{9}{11}\)
B. \(\frac{18}{77}\)
C. \(\frac{1}{2}\)
D. \(\frac{11}{12}\)

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Correct Answer: Option B

Explanation

1st bag → 4 W, 3 B = 7 marbles
2nd bag → 5 R, 6 B = 11 marbles
The only possible way of picking marbles of the same colour is to pick a blue marble from each bag

therefore, Pr( same colour) = \(\frac{3}{7}\times \frac{6}{11} = \frac{18}{77}\)

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