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.

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) (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.
----------------
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
---------------------------------
So, P(neither will purhase) = 1 - (0.03+0.37+0.36) = 0.24
-----------------------------------------------------------
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.
================================================
Cheers,
Stan H.
RELATED QUESTIONS
There is a .45 probability that John will purchase a new car, a .35 probability that Mary (answered by stanbon)

A company sells two products, A and B. The probability that a customer will purchase... (answered by ikleyn)

(a) The probability es that a customer will purchase a new car from Green, white, red or... (answered by ikleyn)

The probability John buys a car is .3 and the probability that Jane buys a car is .2.... (answered by ikleyn)

4. Claire is considering investing in a new business. In the first year, there is a... (answered by Boreal)

The probability that Sue will live on campus and buy a new car is 0.37. If the... (answered by Dickiedannie)

The probability that sue will live on campus and buy a new car is 0.34. If the... (answered by ikleyn)

There is an area of free (but illegal) parking near an inner-city sports arena. The... (answered by ewatrrr)