An experiment succeeds twice as often as it fails. The probability that in the next six trails threr are at most 2 successes, is

Options

A. `(73)/(729)`
B. `(72)/(729)`
C. `(71)/(729)`
D. `(70)/(729)`

Answer

A

Explanation

(a) Let p be the prpobaility of success in a trial.
We have, `" " p=2(1-p) rArrp=(2)/(3)" "[`:'` p=2q]`
The probability of r success in six trails is given by
`P(X=r)=""^(6)C_(r )((2)/(3))^(r )((1)/(3))^(6-r)=""^(6)C_(r )2^(r )((1)/(3))^(6)`
`:. ` Required probability `=p(X le 2)`
`=P(X=0)+P(X=1)+P(X=2)`
`=((1)/(3))^(6)(""^(6)C_(0)xx2^(0)+""^(6)C_(1)xx2^(1)+""^(6)C_(2)xx2^(2))`
`(1+12+60).(1)/(729)=(73)/(729)`