Math 150 Sample Exam #2

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1 Problem 1. (16 points) TRUE or FALSE. a. 3 die are rolled, there are 1 possible outcomes. b. If two events are complementary, then they are mutually exclusive events. c. If A and B are two independent events, then P (A and B) = P (A) P (B). d. If a family has three children, the probability that two of them are girls is 3. e. Two dice are rolled, Event A is getting a sum greater than 10, and event B is getting a sum of odd number. Event A and event B are mutually exclusive. f. The arrival time of a student in a classroom 10 minutes after the scheduled beginning time of class is an example of continuous random variable. g. In a binomial experiment, if the probability of success is 0.7, the probability of failure is 0.3. h. A random variable with binomial distribution is a discrete random variable. Problem 2. (12 points) Two die are rolled. a. What is the probability of getting a sum of odd number? b. What is the probability of getting a sum that is at least 2? c. What is the probability of getting a sum that is odd or less than?

2 Problem 3. (20 points) Suppose that two balls are randomly drawn in succession, without replacement, from a box containing 7 red and green balls. a. Complete and label the tree diagram as follows that will describe the probabilities of the various outcomes. Fill your answers in the boxes provided. Red Start Red Green Green Red Green First Draw Second Draw b. Give the following values: P (2 nd Green 1 st Red) = P (1 st Green and 2 nd Red) = c. What is the probability of getting two of different colors?

3 Problem 4. (10 points) Suppose you plan to insure your new laptop computer, which you will be taking to campus, against theft for the amount of $2000. An insurance company claims that their records indicate 0.2% of such computers on college campuses are stolen within one year and offers to insure. If the insurance company wants to maintain expected earnings of $200 per such policy, what should the premium be? Problem 5. (10 points) In a hospital unit, there are 14 nurses and 6 physicians. nurses and 4 physicians are females. Staff Females Males Nurses 6 Physicians 4 2 If a staff person is selected, a. Find the probability that the subject is a nurse or male. b. Find the probability that the subject is female physician. c. If two people are selected without replacement, what is the probability that both are female physicians?

4 Problem 6. (12 points) Determine whether the given table represents a probability distribution for a random variable. State the reasons. A. X P(X) B. X P(X) C. X P(X)

5 Problem 7 (10 points) A ski loses $70,000 per season when it does not snow very much and makes $250,000 in profit when it does snow at lot. The probability of it snowing at least 75 inches (a good season) is 40%. If the random variable X that represents the earnings of the ski resort. A. Find the probability distribution for the random variable X. B. Find the expected values (mean) for the ski resort. Problem ( points) There is a binomial experiment with the following numbers: The fixed number of trial is n = 12; Every trial is independent of any other trial; There are only two possible outcomes for each trial, success (S) or failure (F); The probability of success (S) are the same for all trials, which is p = P(S) = 0.. X : the number of successes, then A. List all the possible values of X : { } B. Set up the probability of X successes if X = 7:

6 Problem 9. (10 points) It is believed that 90% of the people interviewed got the H1N1 vaccine. If 10 people are selected at random, A. Find the probability that exactly 7 people interviewed got the H1N1 vaccine (use the table provided). B. Find the probability that at least 2 people interviewed got the H1N1 vaccine (use the table provided). C. Find the expected number of people interview got the H1N1 vaccine. D. Find the standard deviation of the number of people interview got the H1N1 vaccine.

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