In: Statistics and Probability
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) = 0.13,
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 1 but neither 2 or 3 awarded 3 but neither 1 nor 2 awarded at least one of these three projects awarded all of the three projects awarded none of the three projects
Compute the probability of this event.
(d)
A1' ∩ A2' ∩ A3'
Express in words the event.
awarded 1 but neither 2 or 3 awarded 3 but neither 1 nor 2 awarded at least one of these three projects awarded all of the three projects awarded none of the three projects
Compute the probability of this event.
(e)
A1' ∩ A2' ∩ A3
Express in words the event.
awarded 1 but neither 2 or 3 awarded 3 but neither 1 nor 2 awarded at least one of these three projects awarded all of the three projects awarded none of the three projects
Compute the probability of this event.
(f)
(A1' ∩ A2') ∪ A3
Express in words the event.
awarded only 1 or 2 awarded only 3 awarded neither of 1 and 2, or awarded 3 awarded either of 1 or 2, but not awarded 3 awarded at least one of these three projects
Compute the probability of this event.