There are 10 beads in a bag. Four beads are green, six are black. If three beads are taken at random without replacement, what is the probability that they are the same colour?

There are two possible outcomes in which all beads are the same colour: they may be all green, or all black. We need to work out the probability of each outcome to start with. This is done by multiplying together the probability of withdrawing Green, Green, Green or Black, Black, Black successively. Probability of 3 green beads removed: (4/10)(3/9)(2/8) = 1/30. Probability of 3 black beads removed: (6/10)(5/9)(4/8) = 1/6. We then add together the probabilities of the possible outcomes to find the probability that the beads are the same colour, regardless of whether they are all green or all black: 1/30 + 1/6 = 1/5 or 0.2.