Theory question 105
ProbabilityOut 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 the three are bad; (c) all the three are good.
Show the model answer
Model answer
P(bad) = 6/24 = 1/4, P(good) = 3/4; with replacement the draws are independent.
(a) 3/4 × 3/4 × 1/4 = 9/64.
(b) (1/4)3 = 1/64.
(c) (3/4)3 = 27/64.
Explanation
With replacement the probabilities stay the same for each draw, so multiply.