Four bricks are sampled from a large load and the crushing strength of each is measured to determine whether it meets a specification. If any of the four fail to meet the specification, the load will be returned. If in fact 10% of the bricks in the load fail to meet the specification, what is the probability that the load will be returned?
What will be an ideal response?
Let R be the event that the shipment is returned. Let 
be the event that the first brick chosen meets the specification, let 
be the event that the second brick chosen meets the specification, let 
be the event that the third brick chosen meets the specification, and let 
be the event that the fourth brick chosen meets the specification. Since the sample size of 4 is a small proportion of the population, it is reasonable to treat these events as independent, each with probability 0.9.
P(R) = 1 – P(Rc) = 1 – P(B1? B2? ?3? ?4)=1 – (0.9)4= 0.3439.
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