Question

At a local auto parts store, the economy ball joints have questionable quality. In the supply the 20 at the stir 7 are unstable for install in a vehicle.

A. If 4 customers purchase ball joints from the supply (1 joint per customer for a total of 4) what is the probability that at most one of the customers will need to return for a replacement?

B. From part a) assume that a customer did in fact need to return one of the joints (no other customer need to return). What is the probability this customer will need to return again if they decide to buy 2 joints the second time (both joints defective)

C. Upon installing a non-defective ball joint in his car, Ralph forgets to properly torque the lug nuts on his wheel. If the wheel has a 5 lug pattern what is the probability that he will make it exactly 15 miles back to the parts store to return the extra ball joint if the probability a lug will come off in any given mile is .25? (Wheels fall off in parking lot when he locks the door) You may assume the lugs will not fall off at the same time.

Answer 1

A) p= probability of defective ball joint.

    X is the number of defective ball joints.

P(at most one need to return for a replacement)=

                                                                                            

=0.56298.

B) Let A be the event: Out of 4 one is defective

       B                   : Out of 2 two are defective

    =0.1225

C) P(lug will not come off in a mile)=0.75

   P(any of the lugs will not come off in 15 miles)=(0.75)¹⁵ X5=0.0668.