First slide

Theorems of probability

Question

A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the
box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is

Moderate

A

5/64
B

27/32
C

5/32
D

½

Solution

The probability of getting a white ball in a single draw is p = 12/24 = 1/2.
The probability of getting a white ball 4ft time in the 7th draw is
P(getting 3w in 6 draws and w in 7th draw)
$=^{6} C_{3} {(\frac{1}{2})}^{6} \frac{1}{2} = \frac{5}{32}$

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