Question

A player throws a fair cubical die and score the number appearing on the die. If he throws a $1$, he gets a further throw. Let $p_r$ denote the probability of getting a total score of exactly $r$. Sum of the series $S=\sum _{r=1}^{\infty }{p}_r$ is

• A. 1
• B. 1/6
• C. 1/5
• D. 2/3

Answer 1

The correct option is C 1/5

Let $P_r$ denote the probability of getting a total score of exactly.

$\Rightarrow A=$ Number appearing on the die.

$\Rightarrow B=$ He throws a one and get a further throw

$=P\left(\frac{A}{B}\right)$

$=$ Probability of occurrence of $A$ when $B$ is taken as the sample space,

$=\frac{No.ofelementaryeventsfavorabletoAwhicharefavorabletoB}{No.ofelementoryeventsfavorabletoB}$

$=\frac{No.ofelementseventsfavorableto(A\cap B)}{No.ofelementoryeventsfavorabletoB}$

$=\frac{1}{5}.$

Hence, the answer is $\frac{1}{5}.$