A computer consulting firm presently has bids out on three projects. Let A, = {a

Question

A computer consulting firm presently has bids out on three projects. Let A, = {awarded project/), for: 1, 2, 3, and suppose that P(A) 0.22, PA2)-0.25, PA30.28, PIA1 A2) 0.15, P nA3)0.05, PIA2A3)0.05, PA nA2nA3)0.01. Express in words each of the following events, and compute the probability of each event. (a) A1 UA Express in words the event. O awarded only 1 O awarded only 2 O awarded neither 1 nor 2 awarded either 1 or 2 O awarded either 1 or 2 (or both) Compute the probability of this event. (b) A1,NA2. [Hint: (A 1 UA2), Express in words the event. O awarded only 1 A1"NA2 awarded only 2 O awarded neither 1 nor 2 awarded either 1 or 2 O awarded either 1 or 2 (or both)

Explanation / Answer

a)

awarded either 1 or 2 (or both)

P(A1 U A2) =P(A1)+P(A2)-P(A1 n A2)=0.22+0.25-0.15=0.32

b)

awarded neither 1 nor 2

A1' n A2' =(A1 u A2) ' =1-0.32 =0.68

c)

awarded at least one of the three projects

P(A1 u A2 uA3 )=P(A1)+P(A2)+P(A3)-P(A1 n A2)-P(A1 nA3)-P(A2 nA 3)+P(A1 nA2 nA3)

=0.22+0.25+0.28-0.15-0.05-0.05+0.01=0.51

d)

awarded none of three projects

P(A1' n A2' nA3' )=1-P(A1 u A2 uA3 ) =1-0.51 =0.49

e)awarded 3 but neither 1 or 2

P(A1' n A2' nA3) =P(A3)-P(A3 n A2)-P(A1 nA2)+P(A1 n A2n A3)=0.19

f)

awarded neither of 1 and 2 or awarded 3

P(A1' n A2' UA3) =0.68

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.