Question

A man throws a die until he gets a number bigger than 3. The probability that he gets 5 in the last throw

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{6}$
• D. $\frac{1}{36}$

Answer 1

The correct option is A $\frac{1}{3}$

P(getting a number bigger than 3) =$\frac{1}{2}$
P(getting 5 in throw)= $\frac{1}{6}$
$E\to getting$ 5 in last throw when he gets a number bigger than 3
$P\left(E\right)=\frac{1}{6}+\frac{1}{2}.\frac{1}{6}+\frac{1}{2}.\frac{1}{2}.\frac{1}{6}+...\infty =\frac{1}{6}\times \frac{1}{1-\frac{1}{2}}=\frac{1}{3}$