Question

Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to:

• A. \(\frac {5}{11}\)
• B. \(\frac {5}{6}\)
• C. \(\frac {1}{11}\)
• D. \(\frac {6}{11}\)

Answer 1

The Correct Option is A

The correct option is (A): \( \frac {5}{11} \)
Let P(2 obtained on even numbered toss) = k.
\( P(2) = \frac{1}{6} \)
\( P(\overline{2}) = \frac{5}{6} \)
\( k = \frac{5}{6} \times \frac{1}{6} + (\frac{5}{6})^3 \times \frac{1}{6} \times (\frac{5}{6})^5 \times \frac{1}{6} + .... \)
\( = \frac{\frac{5}{6} \times \frac{1}{6}}{1 - (\frac{5}{6})^2} \)
\( = \frac{5}{11} \)