A man takes a forward step with probability (.8) and backward step with probability (.2). What is the probability that at the end of 9 steps he is exactly three steps away from starting points ?

Options

A. `(69888)/(5^(8))`
B. `(5377)/(5^(8))`
C. `(5378)/(5^(8))`
D. `(5376)/(5^(8))`

Answer

A

Explanation

(a)`P(X=x)=""^(9)C_(x)(.7)^(x)(.2)^(9-x)`
`=""^(9)C_(6)(,8)^(6)(.2)^(3)+""^(9)C_(3)(.8)^(3)(.2)^(6)`
`=""^(9)C_(6)(.2)^(3)(.8)^(3)[(.8)^(3)+(.2)^(3)]`
`=""^(9)C_(6)(.2)^(3)(.8)^(3)[(4^(3))/(5^(3))+(1)/(5^(3))]`
`=""^(9)C_(6)((1)/(5))^(3)((4^(3))/(5^(3))).(65)/(5^(3))=(69888)/(5^(8))`