pushpitkc wrote:
Hi
dave13Attachment:
Set(s).png
Given: P(Neither) = 5 | P(All 3) = 5
What we need to understand while solving problems like these is that
P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3)
P(Sunporch) = 0.5(150) = 75 =
P(Only SunPorch) + B + C + P(All 3)P(SwimmingPool) = 0.3(150) = 45 = P(Only SwimmingPool) + B + C + P(All 3)
P(Total) = P(Only Airconditioner) + P(Only SunPorch) + P(Only SwimmingPool) + (A + B + C) + P(All 3)
150 = 90 + 75 + 45 - (A + B + C) - 2*P(All 3) + 5
Therefore, the houses which have only two amenities are P(Only 2) = A + B + C = 205 - 150 = 55
(Option D)Hope this helps you!
pushpitkc , generis many thanks for explanation, almost got it
appreciate!
pushpitkc , just one question. Didnt you make a typo here (see highlighted part of your solution above or below
)
P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3)
P(Sunporch) = 0.5(150) = 75 =
P(Only SunPorch) + B + C + P(All 3)P(SwimmingPool) = 0.3(150) = 45 = P(Only SwimmingPool) + B + C + P(All 3)
Lets start from case #1: this one one
P(Airconditioner) = 0.6(150) = 90 = P(Only Airconditioner) + A + B + P(All 3) I interpert it as follows: So there are 90 houses with air conditioning among which are houses featuring only Airconditioner, OR both amenties Airconditioner+Porch and Airconditioner + Swimming pool OR three amenites. Am i understanding it correctly ?
If the above mentioned information i understand correctly, then why here P(Sunporch) = 0.5(150) = 75 =
P(Only SunPorch) + B + C + P(All 3) are you adding up
+ B + C + P(All 3) and not +A+C+(All 3) ? As per your diagram Sunporch has intersection with air conditioning and swimming pool. I am just following the pattern as in case #1.
Case # 1 has intersection with A, B and P so you added A + B + P(All 3)
But case # 2 has this intersection +A+C+P but you sum up B + C + P
i would appreaciate if you could expain this
Further to the above questions can you please confirm if the detaled solution based on suggested formula is correct
pls see below
\(150 = 90+75+45 -(A+B+C)-2(5) +5\)
\(150= 210-(A+B+C)-10+5\)
\(150= 210 -A-B-C-5\)
many thanks and have a great day
\(A+B+C = 55\)