(25 points) suppose the probability of exposure to the flu during an epidemic is 0.6. a vaccine is 80% successful in preventing an inoculated person from acquiring the flu, if exposed to it. a person not inoculated faces a probability of 0.9 of aquiring the flu, if exposed to it. define the probability of at least one will be flue for a randomly selected person.

The probability of at least one person will catch the flu is 0.5952

Step-by-step explanation:

To find the probability of al least one catches the flu, we need to find the difference between 1 and the probability of not catching the flu.

The probability of catching the flu varies if the person is inoculated or not.

Let the events be:

E: the person was exposed

F: the person catches the flu

Hence, it is attached a tree diagram of the sample space. According to the diagram:

Inoculated person:

P(F')= 0.6×0.8 + 0.4×1 = 0.88 (We choose the second and the fourth way)

Not inoculated person:

P(F')= 0.6×0.1 + 0.4×1= 0.46 (We choose the second and the fourth way)

Let the events be:

= the person is inoculated and catches the flu

=the person is not inoculated and catches the flu

Using complementary events, DeMorgan’s Laws, and independence we have:

P(∪)=1-P(∪)'

=1 - P(∩)

=1 - P()×P()

=1 - (0.88)×(0.46)

=1 - 0.4048

=0.5952

The probability of at least one will catch the flu for a randomly selected person is 0.5952

line or a linear equation graph

step-by-step explanation:

true

explanation: