The probability a household in a community uses gas for cooking is 0.18. If a shopper from the community is from a household that uses gas for cooking, there is a 0.7 probability the person shops at Prime Foods. If a shopper is from a household that does not use gas for cooking, there is a 0.35 probability the person shops at Prime Foods. If a person from the community does not shop at Prime Foods, what is the probability gas is used for cooking at that household

The probability of a person from the community not shopping at Prime Foods given that he uses gas for cooking at his household is 0.092

Step-by-step explanation:

Hello!

Given the information:

A: "The household uses gas for cooking" ⇒ P(A)= 0.18

B: "The person from the comunity shops at Prime Foods"

The person shops at Prime Foods given that he uses gas for cooking:

P(B/A)= 0.7

The person shops at Prime Foods given that he doesn't use gas for cooking:

P(B/Ac)= 0.35

If the person doesn't shop at Prime Foods, what is the probability that he uses gas for cooking?

Symbolically:

P(A/Bc) = P(A∩Bc)

                   P(Bc)

The event Bc is the complement of event B, so it's probability is P(Bc)= 1 - P(B)

You can calculate the probability of B as:

P(B)= P(A∩B)+ P(Ac∩B)

Using the information of P(B/A)= 0.7 and P(B/Ac)= 0.35 you can reach the values of both intersections.

P(B/A)= P(A∩B)

                P(A)

P(B/A)*P(A)= P(A∩B)

P(A∩B)= 0.7*0.18= 0.126

and

P(B/Ac)= P(Ac∩B)

                 P(Ac)

If A and Ac are complementary events, then P(Ac)= 1 - P(A)= 1 - 0.18= 0.82

Then:

P(B/Ac)*P(Ac)= P(Ac∩B)

P(Ac∩B)= 0.35*0.82= 0.287

The probability of B is:

P(B)= P(A∩B)+ P(Ac∩B)= 0.126+0.287= 0.413

P(Bc)= 1 - P(B)= 1 - 0.413= 0.587

And

P(A)= P(A∩B)+P(A∩Bc)

P(A∩Bc)=P(A)=-(A∩B)= 0.18-0.126= 0.054

Finally:

P(A/Bc) = P(A∩Bc) =0.054 = 0.0919≅ 0.092

                   P(Bc)     0.587

I hope it helps!

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation:

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step-by-step explanation: