Jee Main 2024 29 01 2024 Shift 1 - Question1
Question 1
Let a die rolled till 2 is obtained. The probability that 2 obtained on even numbered toss is equal to
(1) $\frac{5}{11}$
(2) $\frac{5}{6}$
(3) $\frac{1}{11}$
(4) $\frac{6}{11}$
Show Answer
Answer: (1)
Solution:
$P(2$ obtained on even numbered toss $)=k$ (let)
$$ \begin{aligned} & P(2)=\frac{1}{6} \\ & P(\overline{2})=\frac{5}{6} \\ & k=\frac{5}{6} \times \frac{1}{6}+\left(\frac{5}{6}\right)^{3} \times \frac{1}{6}+\left(\frac{5}{6}\right)^{5} \times \frac{1}{6}+\ldots \\ & =\frac{\frac{5}{6} \times \frac{1}{6}}{1-\left(\frac{5}{6}\right)^{2}} \\ & =\frac{5}{11} \end{aligned} $$
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