Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that :
(a) the first two are good and the third is bad ;
(b) all three are bad ;
(c) all the three are good.
Explanation
(a) (P(Good) = frac{18}{24} = frac{3}{4})
(P(Bad) = frac{6}{24} = frac{1}{4})
P(2 are good and 1 bad) = (frac{3}{4} times frac{3}{4} times frac{1}{4})
= (frac{9}{64})
(b) P(the 3 are bad) = (frac{1}{4} times frac{1}{4} times frac{1}{4})
= (frac{1}{64})
(c) P(the 3 are good) = (frac{3}{4} times frac{3}{4} times frac{3}{4})
= (frac{27}{64})