Probability
Geometric Series — Probability of Success on Even Throw
nta_pyq_2024_jan
Grade 12
Question:
A fair die is thrown until 2 appears. Then the probability that 2 appears in even number of throws is:
$\dfrac{5}{6}$
$\dfrac{1}{6}$
$\dfrac{5}{11}$
$\dfrac{6}{11}$
Step-by-Step Solution
Key Concept: 2 appears on throw 2, 4, 6, ...: $P=\sum_{k=1}^\infty(5/6)^{2k-1}(1/6)=\frac{5/6\cdot1/6}{1-(5/6)^2}$.
$P=\frac{5/36}{11/36}=\frac{5}{11}$.
Correct Answer: 3