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Explain what is wrong and why it is wrong:
1. You bought 10 lottery tickets. One of them won a prize. That means that the probability of winning a prize is 1/10.
--The probability of winning depends on the sample space (the set of all possible n choices if a lottery ticket contains n whole numbers.) That is much larger than 10.
2.In a lottery, buying more tickets does not affect your chances of winning a prize.
--Chances are higher because the size of the subset of possible winning numbers is greater.
3. John has 3 suits, 10 shirts, and 12 neckties. He will need to buy some more clothes if he wants to come to work each work day in a different outfit for a whole year.
--He doesn't need to buy some more clothes, because he can suit up differently for 3*10*12 = 360 days.
4. If in a probability distribution you get the sum of probabilities less than one, it just means that you have a smaller-than-normal distribution.
--The sum of probabilities has to be 1, or else it's not a probability distribution.
5. From the perspective of the insurance company, health insurance policies are set up in such a way that a healthy person has a negative expected value, and a sickly person has a positive one.
--If this were the case, the insurance company would lose money by paying claims from sick policyholders all the time, and would be embezzling money from healthy policyholders.
6. For a given data set, the mean and median are always nearly equal.
--If the data set is heavily skewed to the right, mean > median. If the data set is heavily skewed to the left, mean < median.
7. In the same set of data, no two may have the same z score.
--Repetition of z-scores is possible, because there may be repetition of sample points from which the z-scores came.
8. A negative z score is unusual.
--A negative z-score simply says that the sample point is less than the mean of the data set, which is not unusual.
9. For a set having only negative values, both the mean and standard deviation will be negative.
--Standard deviation is always positive, as it is the square root of the variance of the data set.