There exists 4 bacteria in your shoes at time t=0 seconds.

A bacteria replicate into 2 with a probability p and otherwise die every second.

What is the expected number of bacteria's at the end of 70 seconds.

**Constraints:**

(0<=p<=1)

And you have to report the floor of the answer.

I saw this question on a test which allowed usage of computer but I think it can be done using total maths too.

I thought of doing a dp with state { time , number of bacteria's } which is exponential in nature.

Either way I don't have a solution.

Obviously, if we can solve it for 1 bacteria we can solve it for 4 too but this isn't a significant improvement either .