Question

In: Statistics and Probability

A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project...

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.

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