JAMB 1985 · UME · Q44

A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

Worked solution (try it first)

The first ball is red with probability $\frac{6}{10}$ .
Without replacement, 5 red balls are left out of 9, so the second is red with probability $\frac59$ .
Multiply: $\frac{6}{10} \times \frac59 = \frac{30}{90}$
$= \frac13$ , option A.