Question

A dice is thrown. The probability that the first time 1 occurs at the even throw is A. `1//6` B. `5//11` C. `6//11` D. `5//36` Select the correct answer from above options

Answer 1

Correct Answer - B Let E be the event of getting 1 on a die . `implies P(E ) =(1)/(6) and P(bar (E )) =(5)/(6)` `:.` P (first time 1 occurs at the even throw ) `=t_(2) or t_(4) or t_(6) or t(8) …… and ` so on `={P(bar( E)) P(E ) }+{P(bar( E))P(bar(E )) P(bar(E )) }+ ... oo ` `((5)/(6))((1)/(6))+((5)/(3))^(3)((1)/(6))+((5)/(6))^(5)((1)/(6))+oo=((5)/(36))/(1-(25)/(36))=(5)/(11) `