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

# 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

1. A

$150/{6}^{5}$

2. B

$225/{6}^{5}$

3. C

$175/{6}^{5}$

4. D

$200/{6}^{5}$

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### Solution:

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

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

$\therefore$ Required Probability

$={\left(\frac{5}{6}\right)}^{3}{\left(\frac{1}{6}\right)}^{2}{+}^{2}{C}_{1}{\left(\frac{5}{6}\right)}^{2}{\left(\frac{1}{6}\right)}^{3}=\frac{1}{6}\left({5}^{3}+2×{5}^{2}\right)=\frac{175}{{6}^{5}}$

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