### JEE Main 12 Jan 2019 Morning Question 18

##### Question: 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 [JEE Main Online Paper Held On 12-Jan-2019 Morning]

#### Options:

A) $ \frac{150}{6^{5}} $

B) $ \frac{225}{6^{5}} $

C) $ \frac{175}{6^{5}} $

D) $ \frac{200}{6^{5}} $

## Show Answer

#### Answer:

Correct Answer: C

#### 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 $ ={{( \frac{5}{6} )}^{3}}{{( \frac{1}{6} )}^{2}}{{+}^{2}}C _1{{( \frac{5}{6} )}^{2}}{{( \frac{1}{6} )}^{3}} $ $ =\frac{1}{6^{5}}(5^{3}+2\times 5^{2})=\frac{175}{6^{5}} $