Question

A batch contains 31 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).What is the probability that all six cells of the selected cells are able to replicate

Answer 1

Answer:

0.0369 = 3.69% probability that all six cells of the selected cells are able to replicate.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes

The combinations formula is important in this problem:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes

31 cells

19 are able to replicate.

We pick six.

The order is not important, that is, if it had been 2 cells, cell A and cell B would be the same outcome as cell B and cell A. So we use the combinations formula to find the number of desired outcomes.

It is a combination of 6 from 19(cells who are able to replicate).

$D = C_{19,6} = \frac{19!}{6!(19 - 6)!} = 27132$

Total outcomes

31 cells

6 are picked.

$T = C_{31,6} = \frac{31!}{6!(31 - 6)!} = 736281$

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

$P = \frac{D}{T} = \frac{27132}{736281} = 0.0369$

0.0369 = 3.69% probability that all six cells of the selected cells are able to replicate.

Answer 2

Answer:

The answer would be 98.8

Step-by-step explanation:

Resin being you must round simply to the nearest hundreds