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 amoeba population will be maximum after completion of 3 s is

Options

A. `1//16`
B. `1//8`
C. `3//4`
D. `1//2`

Answer

B

Explanation

After 2 s, exctly 4 amoeba are alive, i.e., initially amoeba must split into two and in 2nd second again amoeba must split into two. Hence, the required propability is `(1//2)xx(1//2)xx(1//2)=1//8.`