A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P (A1) = 0.22, P (A2) = 0.25, P (A3) = 0.28, P (A1 ∩ A2) = 0.12, P (A1 ∩ A3) = 0.03, P (A2 ∩ A3) = 0.06, P (A1 ∩ A2 ∩ A3) = 0.01. Express in words each of the following events, and compute the probability of each event. (a) A1 ∪ A2

(a) P (A1 ∪ A2) = 0.35

Step-by-step explanation:

(a) A1 ∪ A2:

We start by defining the events.

A1 : '' awarded project 1''

A2 : ''awarded project 2''

A3: ''awarded project 3''

In set theory we write the union of events A and B as A∪B.

A∪B means that the event A occurs, event B occurs or either both events occurs at the same time.

The probability is given by the equation:

P (A∪B) = P (A) + P (B) - P (A∩B) (1)

Where the event (A∩B) is the event where A and B occur at the same time

and P (A∩B) is the probability of (A∩B)

Using the equation (1):

P (A1 ∪ A2) = P (A1) + P (A2) - P (A1∩A2)

P (A1 ∪ A2) = 0.22 + 0.25 - 0.12

P (A1 ∪ A2) = 0.35