A box contains 5 white, 7 black and 8 red balls. A ball is drawn at random, its colour is noted and it is put back; this is repeated 300 times. In about how many of these draws would you expect a black ball?

The box holds 5 + 7 + 8 = 20 balls, so P(black) = 7/20 on every draw, the ball being replaced each time. The expected count is $300\times 7/20=105$. Treating the three colours as equally likely gives 300 ÷ 3 = 100, which ignores that the colours are not equally many; using 15 as the total, that is 7 + 8 with the white balls left out, gives $300\times 7/15=140$; and 150 is simply half. An expected count is a long-run average, so the actual number of black balls in one run of 300 draws will vary a little around 105.