Answer Happy

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) = 0.11,
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
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.
(b)
A1' ∩ A2' [Hint: (A1 ∪ A2)' = A1' ∩ A2']
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.
(c)
A1 ∪ A2 ∪ A3
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.
(d)
A1' ∩ A2' ∩ A3'
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.
(e)
A1' ∩ A2' ∩ A3
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.
(f)
(A1' ∩ A2') ∪ A3
Express in words the event.
awarded only 1
awarded only 2
awarded neither 1 nor 2
awarded either 1 or 2
awarded either 1 or 2 (or both)
Compute the probability of this event.