A bag contains only 8 beads. The beads are identical in all respects except colour. 3 of the beads are black and the other 5 beads are white. A bead is taken at random from the bag and not replaced. A second bead is then taken at random from the bag. What is the probability that both beads are black?

Answer:

4) B

Number of beads = 8
Number of black beads = 3

Probability of picking a black bead first time = 3/8

Since the bead is not replaced, the bag now contains 7 beads in total.

Since a black bead would have been taken out, there would be 2 black beads left in the bag out of the total 7 beads.

Probability of picking a second black bead = 2/7

Probability of both beads being black = (3/8 x 2/7) = 6/56 = 3/28