There are four cups. Each cup holds 1 black ball and 1 white ball. You draw one ball from each cup . What is the probability of drawing at least one black ball?

Answer 1

It is the same as the probability of not getting all four white ones..

Probability of all four being white is 1 / 16

Probability of at least one black, 15 / 16/

Answer 2

Hi Eli S.,

No problem! These questions look formidable -- gee, how many ways could I have of drawing a black ball? -- but there is an easy path to the calculation and answer. It's this: you will always draw at least one black ball UNLESS you draw all white balls (i.e. 4 white balls in a row). The odds of the latter happening are sequential, P = (0.5)*(0.5)*(0.5)*(0.5) = 0.0625; thus the odds of the former happening (getting at least one black ball) are 1 - 0.0625 = 0.9375 .

-- Cheers, -- Mr. d.