JAMB 2003 · UME · Q43

A bag contains 5 black balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and a red ball are picked?

Worked solution (try it first)
  1. Black then red: 58×37=1556\frac58 \times \frac37 = \frac{15}{56}, since after one black, 7 balls are left.
  2. Red then black: 38×57=1556\frac38 \times \frac57 = \frac{15}{56}.
  3. Add the two orders: 3056=1528\frac{30}{56} = \frac{15}{28}, option D.

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