A computer consulting firm presently has bids out on threeprojects. Let

A_i = {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 theprobability of each event.

(a)

A₁ ∪ A₂

Express in words the event.

awarded only 1 awarded only 2    awardedneither 1 nor 2 awarded either 1 or 2 awarded either 1 or 2 (orboth)

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    awardedneither 1 nor 2 awarded either 1 or 2 awarded either 1 or 2 (orboth)

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 nor2    awarded at least one of these threeprojects awarded all of the three projects awarded none of thethree 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 nor2    awarded at least one of these threeprojects awarded all of the three projects awarded none of thethree 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 nor2    awarded at least one of these threeprojects awarded all of the three projects awarded none of thethree projects

Compute the probability of this event.

(f)

(A₁' ∩ A₂') ∪ A₃

Express in words the event.

awarded only 1 or 2 awarded only3    awarded neither of 1 and 2, or awarded 3awarded either of 1 or 2, but not awarded 3 awarded at least one ofthese three projects

Compute the probability of this event.