in a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

A
$150 / 6^{5}$
B
$225 / 6^{5}$
C
$175 / 6^{5}$
D
$200 / 6^{5}$

Solution:

Let $p$ be the success that die turns up 4.

$∴ p = \frac{1}{6}, q = \frac{5}{6} .$ Here $n = 5$

$∴$ Required Probability

$= {(\frac{5}{6})}^{3} {(\frac{1}{6})}^{2} +^{2} C_{1} {(\frac{5}{6})}^{2} {(\frac{1}{6})}^{3} = \frac{1}{6} (5^{3} + 2 \times 5^{2}) = \frac{175}{6^{5}}$

Solution:

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