Verified Solution • 2025–26 Session moderate

QJEEM24Mad325: JEE Main 2024 Mathematics - Class 12 JEEM24Mad325 Solution: A fair die is thrown until 2 appears. Then the probability,…

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

Multiple Choice Options

  • A 511\frac{5}{11}
  • B 56\frac{5}{6}
  • C 16\frac{1}{6}
  • D 611\frac{6}{11}

Step-by-Step Verified Solution

Required probability ==

amp;56×16+(56)3×16+(56)5×16+…..amp;=16×561−2536=511\begin{aligned}& \frac{5}{6} \times \frac{1}{6}+\left(\frac{5}{6}\right)^3 \times \frac{1}{6}+\left(\frac{5}{6}\right)^5 \times \frac{1}{6}+\ldots . . \\& =\frac{1}{6} \times \frac{\frac{5}{6}}{1-\frac{25}{36}}=\frac{5}{11}\end{aligned}

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