Chapter 4: Q6 (page 178)

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.

Expert verified

The probability that the subject develops flu is 0.0680.

Step by step solution

The data is tabulated for the effectiveness of the vaccine.

One subject is randomly selected.

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

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

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

The row and column totals are computed as follows.

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:

$P (E) = \frac{109}{1602} = 0.06804 \approx 0.0680$

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

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