SOLUTION: The probability that a new automobile has a backup camera is 0.6. The probability that a new automobile has a GPS system is 0.4. The probability that a new automobile has both a ba

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Question 1152147: The probability that a new automobile has a backup camera is 0.6. The probability that a new automobile has a GPS system is 0.4. The probability that a new automobile has both a backup camera and a GPS is 0.2. If a new automobile is selected at random, find the probability that it has neither a backup camera nor a GPS.
Answer by ikleyn(52776) About Me  (Show Source):
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We are given


    P(A) = 0.6   (the probability that a new automobile has a backup camera)

    P(B) = 0.4   (the probability that a new automobile has a GPS system)

    P(A ∩ B) = 0.2   (the probability that a new automobile has both a backup camera and a GPS)


The problem asks about  the COMPLEMENTARY probability to  the event (A U B).


Use the general formula of the probability theory


    P(A U B) = P(A) + P(B) - P(A ∩ B).


Substitute the given data


    P(A U B) = 0.6 + 0.4 - 0.2 = 0.8.


Then the COMPLEMENTARY probability is


    P' = 1 - P(A U B) = 1 - 0.8 = 0.2.


It is your ANSWER : the probability that it has neither a backup camera nor a GPS is equal to 0.2.

Solved.