Paragraph: A fair die is tossed repeatedly until a six is obtained. Let $X$ denotes the number of tosses…

Paragraph: A fair die is tossed repeatedly until a six is obtained. Let $X$ denotes the number of tosses required. Question: The probability that $X=3$ equals
  1. $\frac{25}{216}$
  2. $\frac{25}{36}$
  3. $\frac{5}{36}$
  4. $\frac{125}{216}$

Solution

$P(X=3)=\frac{5}{6} \cdot \frac{5}{6} \cdot \frac{1}{6}=\frac{25}{216}$

Asked in: JEE Advanced 2009 (Paper 1)

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