A biology professor has two graduate assistants helping her

A biology professor has two graduate assistants helping her with her research. The probability that the older of the two assistants will be absent on any given day is 0.08, the probability that the younger of the two will be absent on any given day is 0.05, and the probability that they will both be absent on any given day is 0.02. Find the probabilities that:

a) Either or both of the graduate assistants will be absent on any given day.

b) at least one of the two graduate assistants will not be absent on any given day.

c) only one of the two graduate assistants will be absent on any given day.

Solution

Let

A1 = the older one will be absent
A2 = the younger one will be absent

Thus,

a)

P(A1 U A2) = P(A1) + P(A2) - P(A1 n A2) = 0.08 + 0.05 - 0.02 = 0.11 [answer]

b)

P(at least one will not be absent) = 1 - P(both will be absent) = 1 - P(A n B)

= 1 - 0.02 = 0.98 [answer]

c)

P(only one) = P(A1 only or A2 only) = P(A1) + P(A2) - 2 P(A1 n A2) = 0.08 + 0.05 - 2*0.02 = 0.09 [answer]