Acomputer 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