Answer:
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) =<u> P(A∩Bc) </u>
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)=<u> P(A∩B) </u>
P(A)
P(B/A)*P(A)= P(A∩B)
P(A∩B)= 0.7*0.18= 0.126
and
P(B/Ac)=<u> P(Ac∩B) </u>
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) =<u> P(A∩Bc) </u>=<u>0.054 </u>= 0.0919≅ 0.092
P(Bc) 0.587
I hope it helps!
