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# A bag contains three red and five white balls of equal sizes. Two balls are pick...

### Question

A bag contains three red and five white balls of equal sizes. Two balls are picked at random one after theother without replacement. What is the probability that both balls are of the same color?

### Options

A) $$\frac{13}{32}$$

B) $$\frac{3}{28}$$

C) $$\frac{5}{14}$$

D) $$\frac{13}{28}$$

### Explanation:

Pr(Both balls of the same color) = Pr(Red 1st and Red 2nd) + Pr(White 1st and White 2nd)
$$\left( \cfrac{3}{8} \times \cfrac{2}{7} \right) + \left( \cfrac{5}{8} \times \cfrac{4}{7} \right) = \cfrac{3}{28}+\cfrac{5}{14}=\cfrac{3+10}{28}=\cfrac{13}{28}$$

## Dicussion (1)

• Pr(Both balls of the same color) = Pr(Red 1st and Red 2nd) + Pr(White 1st and White 2nd)
$$\left( \cfrac{3}{8} \times \cfrac{2}{7} \right) + \left( \cfrac{5}{8} \times \cfrac{4}{7} \right) = \cfrac{3}{28}+\cfrac{5}{14}=\cfrac{3+10}{28}=\cfrac{13}{28}$$