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 ...
Question 1 Report
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.
Answer Details
Out of \(24\) apples, \(6\) are bad, so \(18\) are good. Because the drawing is with replacement, each draw is independent with \[P(\text{good}) = \frac{18}{24} = \frac{3}{4},\qquad P(\text{bad}) = \frac{6}{24} = \frac{1}{4}.\]
(a) First two good, third bad: \[\frac{3}{4}\times\frac{3}{4}\times\frac{1}{4} = \mathbf{\frac{9}{64}}.\]
(b) All three bad: \[\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4} = \mathbf{\frac{1}{64}}.\]
(c) All three good: \[\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4} = \mathbf{\frac{27}{64}}.\]
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