SOLUTION: 10.) There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will purchase a new car, and a 0.36 probability that both will purcharse a new car.

Algebra ->  Probability-and-statistics -> SOLUTION: 10.) There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will purchase a new car, and a 0.36 probability that both will purcharse a new car.      Log On


   

Question 184478This question is from textbook Elementary Statistics
: 10.) There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will purchase a new car, and a 0.36 probability that both will purcharse a new car. Find the probability that neither will purchase a new car.
Please help me with this problem. Thanks. This question is from textbook Elementary Statistics

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There is a 0.39 probability that John will purchase a new car, a 0.73 probability that Mary will purchase a new car, and a 0.36 probability that both will purcharse a new car. Find the probability that neither will purchase a new car.
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P(only John will purchase) = 0.39-0.36 = 0.03
P(only Mary will purchase) = 0.73-0.36 = 0.37
P(both will purchase) = 0.36
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So, P(neither will purhase) = 1 - (0.03+0.37+0.36) = 0.24
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You can see this if you draw the Venn Diagram for the problem.
Draw two intersecting circles: one for John and one for Mary.
Put 0.36 in the intersection.
Then John only is 0.03; Mary only is 0.37.
Adding those to the intersection you get 0.76.
That leaves 0.24 outside both circles.
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Cheers,
Stan H.