SOLUTION: A survey of 500 people was conducted to determine how many people own a pet, and how many people own a car. The results showed that 300 people own a pet, 150 people own a car, and

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Question 1204405: A survey of 500 people was conducted to determine how many people own a pet, and how many people own a car. The results showed that 300 people own a pet, 150 people own a car, and 100 people own both a pet and a car. What is the probability that a randomly selected person owns a pet or a car?
P(A or B) = P(A) + P(B) - P(A and B) where P(A) is the probability of owning a pet, P(B) is the probability of owning a car, and P(A and B) is the probability of owning both a pet and a car. Is the answer .70 or .72?
300/500 + 150/500 - 100/500 = 350/500 = 7/10 = .70
300/500 = .60 ; 150/500 = .30 ; (1 - (.60 + .30) = .10 own both a pet a and car
.60 + .30 - (.60 * .30)
0.90 - 0.18 = 0.72
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52760)   (Show Source): You can put this solution on YOUR website!
.

Do not confuse yourself - and do not try to confuse other people. 

P(car or pet) = P(car) + P(pet) - P(BOTH) =  +  -  =   =  =  =  = 0.7.    ANSWER

Solved. 

    Do not try to introduce 0.6*0.3 = 0.18  without necessity, 

         since it relates to INDEPENDENT events ONLY, 

           which is NOT the CASE in this problem.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

A = set of people who own a pet (some also own a car)
B = set of people who own a car (some also own a pet)

n(A) = number of people in set A
n(A) = 300
n(B) = 150
n(A and B) = 100

Use the inclusion-exclusion principle:
n(A or B) = n(A) + n(B) - n(A and B)
n(A or B) = 300 + 150 - 100
n(A or B) = 350
We subtract off 100 because those people were counted twice when computing the n(A)+n(B) portion. The 100 goes in the overlapped portion of the Venn Diagram.

Then,
P(A or B) = n(A or B)/n(Total)
P(A or B) = 350/500
P(A or B) = 0.7

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A slightly different approach

n(A) = 300
n(A and B) = 100
n(A only) = n(A) - n(A and B) = 300-100 = 200
There are 200 people who own a pet, but do not own a car.
This value 200 goes in circle A but outside circle B of the Venn Diagram.

n(B) = 150
n(A and B) = 100
n(B only) = n(B) - n(A and B) = 150-100 = 50
There are 50 people who own a car, but do not own a pet.
This value 50 goes in circle B but outside circle A of the Venn Diagram.

n(A or B) = n(A only) + n(B only) + n(A and B)
n(A or B) = 200 + 50 + 100
n(A or B) = 350
There are 350 people who own a pet, have a car, or both.

The steps from this point onward will be the same as the previous section above.

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Answer: 0.7
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