Question 19

In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?

Solution

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Probability = $$Expected  number  of  outcomes\div Total  number  of  outcomes$$.

Total number of outcomes = Total number of ways to draw randomly 3 balls out of 12 balls = 12C3 ways.

Expected number of outcomes = Number of ways to draw 2 yellow balls out of 8 and 1 black ball out of 4 = $$8C2\times 4C1$$

$$ Hence Probability = 8C2\times 4C1\div 12C3 = 28\times 4\div 220 = \frac{28}{55}$$

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