a)A box holds 8 red and 4 blue beads. Three beads are taken from the box and not replaced. Determine:

(i)The probability that all three beads taken are red

(ii)The probability that there are at least two blue beads from the three that were taken

b)Three machines produce 50%, 40% and 10% respectively, of the total production. The respective percentages of defective production are 2%, 2% and 5%.

i.If an item is selected at random from the collective output of the machines, find the probability that it is defective

ii.If two items are selected at random from the collective output, find the probability that at least one of them is defective