Question

A test tube contains 10⁶ bacteria in suspension and 2 x 10⁶ phage are added to the tube. Each bacterial cell may be infected by 0, 1, 2, 3, ... phage and the number of phage infecting a particular bacterial cell is a random event. Assume all phage infect a bacterial cell. If a bacterial cell is infected by 1 or more phage it will lyse between 20 and 30 minutes after mixing the phage with the bacteria.

What is the average number of phage per bacterial cell?

What proportion of bacterial cells do you predict are not infected by any phage?

What proportion of bacterial cells do you predict are infected by exactly 1 phage?

What proportion of bacterial cells do you predict are infected by 2 or more phage?

What proportion of the bacterial cells do you predict will lyse within 30 minutes after adding the phage to the bacterial suspension?

Answer 1

From the data given there are 212 phage for 106 bacteria in the test tube.

a) The average number of phage per bacterial cell is

b)We can assume that the number of bacterial cells infected by phage follows Poisson distribution ,

The Poisson PMF is

Here .

The probability

c) To find the proportion of bacterial cells that are infected by exactly 1 phage,

The probability

c) To find the proportion of bacterial cells that are infected by infected by 2 or more phage,

The probability

d) Given a bacterial cell is infected by 1 or more phage it will lyse between 20 and 30 minutes after mixing the phage. So the proportion of the bacterial cells that will lyse within 30 minutes after adding the phage to the bacterial suspension is