Suppose the probability of getting the flu is 0.20, the probability of getting a flu shot is 0.60, and the probability of both getting the flu and a flu shot is 0.10.

(a) Find the probability of the union between (getting the the flu) and (getting the flu shot).

(b) Find the probability of (getting the flu and not getting the flu shot).

(c) Find the probability of not getting the flu, and also not getting the flu shot.

(d) Describe the complement of the probability in (a).

a) P (AUB) = 0.20+0.60-0.10 = 0.70

b) P (A only) = P (A) - P (A∩B) = 0.20 - 0.10 = 0.10

c) P (AUB) ' = 1 - P (AUB) = 1 - 0.70 = 0.30

d) d) the complement of the probability of the union between (getting the the flu) and (getting the flu shot) P (AUB) ' is the probability of not getting any of the two cases (neither flu nor flu shot). It is the probability that a person chosen at random would not get any of the two cases. It can be expressed mathematically as;

P (AUB) ' = 1 - P (AUB)

Step-by-step explanation:

Let;

P (A) represent the probability of getting flu

P (B) represent the probability of getting flu shot

P (A∩B) represent the probability of both getting the flu and a flu shot

P (A) = P (A only) + P (A∩B)

P (B) = P (B only) + P (A∩B)

P (AUB) = P (A only) + P (B only) + P (A∩B)

P (AUB) = P (A) + P (B) - P (A∩B) ... 1

Given;

P (A) = 0.20

P (B) = 0.60

P (A∩B) = 0.1

from equation 1

P (AUB) = 0.20+0.60-0.10 = 0.70

b) P (A only) = P (A) - P (A∩B) = 0.20 - 0.10 = 0.10

c) P (AUB) ' = 1 - P (AUB) = 1 - 0.70 = 0.30

d) the complement of the probability of the union between (getting the the flu) and (getting the flu shot) P (AUB) ' is the probability of not getting any of the two cases (neither flu nor flu shot). It is the probability that a person chosen at random would not get any of the two cases. It can be expressed mathematically as;

P (AUB) ' = 1 - P (AUB)