An amobeba either splits into two or remains the same or eventually dies out immediately after completion of evary second with probabilities, respectively, 1/2, 1/4 and 1/4. Let the initial amoeba be called as mother amoeba and after every second, the amoeba, if it is distinct from the previous one, be called as 2nd, 3rd,...generations.
The probability that after 2 s exactly 4 amoeba are alive is

Options

A. `9//32`
B. `11//32`
C. `1//2`
D. `3//32`

Answer

D

Explanation

Let E be the event that all the amoeba population dies out,
`E_(1)` be the evebnt that after fire second amoeba shlite into two,
`E_(2)` be the event that after first second amoeba remains the same. Then
`P(E)=P(E_(1))P(E//E_(1))+P(E_(2))P(E//E_(2))`
`=1/2xx1/4xx1/4+1/4xx1/4=3/32`