You seed a Petri dish with a colony of 1e9 or 1 109 bacteria

You seed a Petri dish with a colony of 1e9 or 1* 10^9 bacteria. Each day, the number of bacteria either:

• stays the same, with probability 2/5;

• doubles, with probability 3/10;

• quadruples, with probability 1/5;

• is divided by a factor of two, with probability 1/10.

Ten days later, what is the probability that there are more than 30e9 or 30 * 10^9 bacteria?

Hint: write number of bacteria as 2^(Summation Xi) , and rewrite the probability you want to obtain into one that can be computed using the normal approximation

Solution