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Four categories are allotted for each subject.

The categories are listed as:

• Developed flu
• Did not develop flu
• Vaccine treatment
• Placebo

The probability for an event is the measure that defines the likelihood of the event.

The probability for any event is determined using the following formula:

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

Compute the sum row-wise and column-wise.

Define A as the event that the randomly selected person is vaccine treated and also develops flu.

Event A is the combination of two simple events:

• X: Subject had vaccine treatment
• Y: Subject developed flu

Thus, $P\left(A\right)=P\left(X\text{and}Y\right)$.

The count of the subjects in the study that had received vaccine treatment and developed flu is 14.

The total number of subjects recorded is 1602.

Using the values, the probability for event A is computed as follows:

$$\begin{gathered} P\left(A\right)=P\left(X\text{and}Y\right) \\ =\frac{14}{1602} \\ =0.00874 \end{gathered}$$

Thus, the probability that the subject in the study had received vaccine treatment and developed flu is 0.00874.