Question

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

• A. $P(x\ge 3)=\frac{25}{36}$
• B. $P(x=3)=\frac{25}{36}$
• C. $P\left(\frac{x\ge 6}{x>3}\right)=\frac{25}{216}$
• D. $P(x<3)=\frac{25}{36}$

Answer 1

The correct option is A $P(x\ge 3)=\frac{25}{36}$

$P(x=3)=\frac{5}{6}.\frac{5}{6}.\frac{1}{6}=\frac{25}{216},P(x<3)=\frac{1}{6}+\frac{5}{6}.\frac{1}{6}=\frac{11}{36}$
$P(x\ge 3)=1-\frac{11}{36}=\frac{25}{36}$
$P\left(\frac{x\ge 6}{x>3}\right)=\frac{P(x\ge 6)}{P(x>3)}=\frac{{\left(\frac{5}{6}\right)}^5.\frac{1}{6}+{\left(\frac{5}{6}\right)}^6.\frac{1}{6}+\cdots \cdots }{{\left(\frac{5}{6}\right)}^3.\frac{1}{6}+{\left(\frac{5}{6}\right)}^4.\frac{1}{6}+\cdots \cdots }=\frac{25}{36}$