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

Options

A. `(175)/(6^(6))`
B. `(225)/(6^(5))`
C. `(200)/(6^(5))`
D. `(150)/(6^(5))`

Answer

A

Explanation

Since, the experiment should be end in the fifth throw of the die, so total number of outcomes are `6^5`
Now, as the last two throws should be result in two fours
`""/(i)""/(ii)""/(iii)4/(iv)4/(v)`
So, the third throw can be l , 2, 3, 5 or 6 (not 4). Also, throw number (i) and (ii) can not take two fours in succession, therefore number of possibililites for throw `(i) and (ii) =6^2-1=35 [therefore ` when a pair of dice is thrown then (4,4) occur only once ]
Hence , the required probility `=(5xx35)/6^5=(175)/6^5`