SOLUTION: The length of the road between A and B is 134 km. The distance from A to the roadside cafe is 36 km, the distance from A to the roadside service is 70 km. What is the probability t

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Question 1191188: The length of the road between A and B is 134 km. The distance from A to the roadside cafe is 36 km, the distance from A to the roadside service is 70 km. What is the probability that in the breakdown of a car, the distance from the place of failure to the service will be less than to the cafe? What is the probability that in the breakdown of two cars, at least one point of failure will be closer to the service than the cafe?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The length of the road between A and B is 134 km.
The distance from A to the roadside cafe is 36 km,
the distance from A to the roadside service is 70 km.
(a) What is the probability that in the breakdown of a car,
the distance from the place of failure to the service will be less
than to the cafe?
(b) What is the probability that in the breakdown of two cars,
at least one point of failure will be closer to the service than the cafe?
~~~~~~~~~~~~~~~


            In this my post,  I will answer question  (a),  only. 


Make a sketch.  
                           70-36=34

     0             36    36+34/2=53     70                          134
                        
     +--------------|---------x---------|---------------------------+
                             
     A             Cafe       M        Service                      B
                           mid-point
                        between C and S


Cafe is 36 km from A;  Service is 70 km from A;  B is 134 km from A.

The distance from C to S is 70-36=34 km.

M is the mid-point between C and S.  Point M is 36+34/2 = 36+17=53 km from A.


The set of points, where the failure is closer to Service than to Cafe is the interval (MB] 
of the length of 134 - 53 = 81 km.


The probability that the place of failure is closer To S than to C is the ratio of the length MB
to the length of AB


    P =  =  = 0.6045 = 60.45%.    ANSWER

Part  (a)  is solved.



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