NECO 2023 · Paper 1 · Q51

Probability

Two balls are taken one after the other without replacement from a bag containing 4 red and 6 blue balls. What is the probability that they are of different colours?

Worked solution (try it first)

Red then blue: $\frac{4}{10} \times \frac69 = \frac{24}{90}$ , since 9 balls are left after the first.
Blue then red: $\frac{6}{10} \times \frac49 = \frac{24}{90}$ .
Add the two orders: $\frac{48}{90} = \frac{8}{15}$ , option B.

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