JEE MAIN - Mathematics (2019 - 12th January Morning Slot - No. 6)
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 :
$${{200} \over {{6^5}}}$$
$${{225} \over {{6^5}}}$$
$${{150} \over {{6^5}}}$$
$${{175} \over {{6^5}}}$$
Explanation
$$\underline {} \,\,\,\underline {} \,\,\,\underline {} \,\,\underline 4 \,\,\underline 4 $$
$${1 \over {{6^2}}}\left( {{{{5^3}} \over {{6^3}}} + {{2{C_1}{{.5}^2}} \over {{6^3}}}} \right) = {{175} \over {{6^5}}}$$
$${1 \over {{6^2}}}\left( {{{{5^3}} \over {{6^3}}} + {{2{C_1}{{.5}^2}} \over {{6^3}}}} \right) = {{175} \over {{6^5}}}$$
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