Answer to Question #295089 in Statistics and Probability for dan

Question

The probability that aa 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 GPS is 0.2. If a new automobile is

selected at random, what is the probability that it has neither a backup camera nor a

GPS?

Answer 1

Let $A$ be the event that the new automobile has a backup camera. Its probability is $p(A)=0.6$

Let $B$ be the event that the new automobile has a GPS. Its probability is $p(B)=0.4$.

The probability that the new automobile has both a backup camera and GPS is $p(A\cap B)=0.2$

We first need to determine $p(A\cup B)=p(A)+p(B)-p(A\cap B)=0.6+0.4-0.2=0.8$

The probability that the new automobile has neither a backup camera nor a GPS is $1-0.8=0.2$

The required probability is 0.2