Question

A microbiologist conducts an experiment to create a recombinant strain of bacteria that is resistant to penicilin. He plates out the bacteria on an agar plate, and picks out 10 colonies each of which consists of clones of a different individual bacterium. He knows that the probability of successfully creating a recombinant per individual bacterium is 0.15. What is the probability that if he mixes all 10 colonies in a growth medium with penicillin something will grow?

Answer 1

This can be solved as a binomially distributed randaom variable with n=10, p =0.15, q = 1-0.15 =0.85

Probability that something will grow = 1-probability that nothing will grow

Probability that nothing will grow, P(X=0) = $\binom{10}{0}0.15^{0}0.85^{10}=1*1*0.1969=0.1969$

Probability that something will grow = 1-0.1969 = 0.8031