Question

A batch contains 37 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that all six cells of the selected cells are able to replicate? (b) What is the probability that at least one of the selected cells is not capable of replication?

Answer 1

Answer:

a) There is a 9.52% probability that all cells are able to replicate.

b) There is a 90.48% probability that at least one cell is not capable of replication.

Step-by-step explanation:

This is a probability problem.

Probability

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

In our problem, there is:

-A $\frac{25}{37} = 0.6757 = 67.57%$ probability that a cell is capable of replication.

-A $\frac{12}{37} = 0.3243 = 32.43%$ probability that a cell is not capable of replication.

(a) What is the probability that all six cells of the selected cells are able to replicate?

For each cell, there is a 67.57% probability that it is able to replicate. So, the probability that all cells are able to replicate is

$P = (0.6757)^{6} = 0.0952 = 9.52%$

(b) What is the probability that at least one of the selected cells is not capable of replication?

-Either all cells are capable of replication or at least one cell is not capable of replication.

-The sum of the probabilities is always 100%.

In (a), we found that the probability that all cells are able to replicate is 9.52%. So the probability of at least one cell not being capable of replication is

$P = 100% - 9.52% = 90.48%$