JEE PYQ: Probability Question 48
Question 48 - 2019 (12 Jan Shift 2)
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) $\frac{200}{6^5}$
(2) $\frac{150}{6^5}$
(3) $\frac{225}{6^5}$
(4) $\frac{175}{6^5}$
Show Answer
Answer: (4)
Solution
The experiment ends at 5th throw with “44” at positions 4,5. Patterns: $* * * 4 4$ where 3rd throw is not 4, or $* * 4 \overline{4} 4 4$… Counting: $4__44$: $\frac{1}{6} \cdot \frac{5}{6} \cdot \frac{5}{6} \cdot \frac{1}{6} \cdot \frac{1}{6}$, etc. $P = \frac{5 \times 5 \times 5 + 5 \times 5 \times 1 + 5^3}{6^5} = \frac{175}{6^5}$.
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