A box contains 5 blue beads, 4 yellow beads and 3 purple beads. Three beads are taken from the bag, at random, without replacement.
a) What is probability of picking, in order, a blue bead followed by a yellow bead followed by a purple bead?
b) Work out the probability that all three beads will be the same colour.
c) What is the probability that the three beads will not be the same colour.
blue = 5 yellow = 4 purple = 3 total = 12
a) blue = 5/12
yellow = 4/11 (only 11 beads remain)
purple = 3/10 (only 10 beads remain)
Multiplying these together: 5/12 x 4/11 x 3/10 =
b) to be three beads of the same color, they could:
-- all be blue: 5/12 x 4/11 x 3/10 = answer #1
-- or all be yellow: 4/12 x 3/11 x 2/10 = answer #2
-- or all be purble: 3/12 x 2/11 x 1/10 = answer #3
Find these three answers and add them together for your final answer.
c) not all of the same color.
-- this will occur when the answer to part b) is false; so, subtract the answer of part b) from 1.000.