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Extra credit problems:
- A pizza house has the following promotional sale. Buy 3 large pizzas at the regular price, then for each pizza you can get as manny different toppings as you wish out of the 9 total toppings offerred. The ad says there're 22 million different ways to choose your pizzas. The pizza house evaluated the number using the formula (29)3/3!. However, this formula is certainly wrong since it does not even produce an integer. What mistake did they make to write this formula? What would be the correct way to evaluate?
- Suppose for a family the probability of having a boy or a girl for each child is equally 1/2.
- The mom told you that one of her two kids is a boy, what is the probability that both kids are boys?
- You got to meet one of the kids (randomly) and found it's a boy, what is the probability that the other kid is also a boy?
- Are these two the same? why or why not?
- Five professors flew from Beijing to Xi'an in China. When they checked
in, the agent handed back the passports randomly. The professors found
that two of them got their own passport and three got the wrong
passport. Being professors, they wondered if this was an unusual
outcome. Suppose P(n) denotes the number of possible ways of distributing n passports among n professors such that none of them gets his/her own passport, develop a recursive representation of P(n).
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