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The probability that any given toy is in the yard is . So the probability that out of toys are in the yard is . You forgot to multiply by . The reason the is there is because there are ways in which this event can happen, depending upon exactly which of the toys is not in the yard. So the probability that Mingus is happy isout of out ofIn general if we want the probability that out of toys are in the yard we use the Binomial Coefficient , and get the probabilitySo, for example, the probability that 3 out of Duke's 5 toys are in the yard is
So work out the probability that or of Duke's toys are in the yard; add these together and set the result to be less than the result for Mingus that I've given you above.
When I do this and simplify the result I get the inequality.This gives the answer .
Do you want to try again and see if you agree with my answer?