1. How are permutations different from combinations? 2. Suppose there are 365

1. How are permutations different from combinations?
2. Suppose there are 365 days in a year and we are ignoring leap years. Suppose there are n property owners’ club of which you are not a member. You can only become a member if the registration date of your property matches with that of any of the n owners.
a. What is the probability of this match (in terms of n)? Hint: find the probability of the complement event.
b. What should n be for chances of the match being 50%? Why may this number be different from 365/2?
c. Suppose they refuse you a membership in the club. For you to challenge them, you need to show that none of the n existing owners have their registration on the same day. What is the probability of this happening? You may leave the answer as an expression, instead of a number.
3. An insurance company finds that Mark has a 8% chance of getting into a car accident in the next year. If Mark has any kind of accident then the company guarantees to pay him $10, 000. The company has decided to charge Mark a $200 premium for this one year insurance policy.
a. Let X be the amount of profit or loss from this insurance policy in the next year for the insurance company. Find EX, the expected return for the Insurance company? Should the insurance company charge more or less on its premium?
b. What amount should the insurance company charge Mark in order to guarantee an expected return of $100? [10%]
4. Suppose that, some time in the distant future, the average number of burglaries in New York City in a week is 2.2. Approximate the probability that there will be
a. no burglaries in the next week;
b. at least 2 burglaries in the next week.
5. A NYU student claims that she can distinguish Van Leewen ice cream from Hagen Dazs’s ice cream. There are 60% chance of her claim to be true.
a. What is the probability that she needs to test 8 samples to guess the ice cream correctly for the first time. How many ice creams does she need to test on average to arrive at the first correct guess?
b. What is the probability her 8th correct guess comes with the 10th sample that she tastes?