Question

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

	Developed Flu	Did not develop Flu
Vaccine Treatment	14	1056
Placebo	95	437

If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.

Short answer

The probability that the subject develops flu is 0.0680.

Step-by-step solution

Given information

The data is tabulated for the effectiveness of the vaccine.

One subject is randomly selected.

Describe the probability of any event

A measure that can determine the likelihood of events is known as probability.

For any event E, the mathematical formula of probability is:

$P\left(E\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Tabulate the row and column totals

The row and column totals are computed as follows.

	Developed Flu	Did not develop Flu	Totals
Vaccine Treatment	14	1056	1070
Placebo	95	437	532
Total	109	1493	1602

Compute the probability of the event

Define an event E that the randomly selected subject developed flu.

Using the tabulated values, compute the probability as follows:

The number of subjects who developed flu is 109.

The total number of subjects recorded is 1602.

So, the probability that the subject developed flu is:

$$\begin{gathered} P\left(E\right)=\frac{109}{1602} \\ =0.06804 \\ \approx 0.0680 \end{gathered}$$

Thus, the probability that the randomly selected subject developed flu is 0.0680.