1. Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probabilities of the following results. (Answer: .9955)
At most one is a queen.
2. In placebo-controlled trials of Prozac®, a drug that is prescribed to fight depression, 23% of the patients who were taking the drug experienced nausea, whereas 10% of the patients who were taking the placebo experienced nausea.*
a. If 50 patients who are taking Prozac® are selected, what is the probability that 10 or more will experience nausea?
b. Of the 50 patients in part a, what is the expected number of patients who will experience nausea?
c. If a second group of 50 patients receives a placebo, what is the probability that 10 or fewer will experience nausea?
d. If a patient from a study of 1000 people, who are equally divided into two groups (those taking a placebo and
those taking Prozac), is experiencing nausea, what is the probability that he/she is taking Prozac?
e. Since .23 is more than twice as large as .10, do you think that people who take Prozac® are more likely to experience nausea than those who take a placebo? Explain.
(Answers: a. about .74 b. about 12 c. about .99 d. about .70)
3. According to officials of Mars, the makers of M&M Plain Chocolate Candies, 20% of the candies in each bag are red. Four candies are selected from a bag and the number of red candies is recorded. (Answer: .8)
Find the expected value
4. In the mathematics honors society at a college, 2 of the 8 members are African American. Three members are selected at random to be interviewed by the student newspaper, and the number of African Americans is noted. (Answer: ¾)
Find the expected value.
5. A lottery has a first prize of $5000, two second prizes of $1000 each, and two $100 third prizes. A total of 10,000 tickets are sold, at $1 each. Find the expected winnings of a person buying 1 ticket. (Answer: -$0.28)
55. On June 23, 2003, an interesting thing happened in the Pennsylvania Lottery's Big 4, in which a four-digit number from 0000 to 9999 is chosen twice a day.* On this day, the number 3199 was chosen both times.
a. What is the probability of the same number being chosen twice in one day?
b. What is the probability of the number 3199 being chosen twice in one day?
(Answers: 1/10,000, 1/100,000,000)
(Answer: a. Stock I: 8%, 7.9%; Stock II: 8%, 2.6% )
6. About 6% of the frankfurters produced by a certain machine are overstuffed and thus defective. Find the following probabilities for a sample of 500 frankfurters. (Answer: .1977, .0718, .0239)
a. Twenty-five or fewer are overstuffed.
b. Exactly 30 are overstuffed.
c. More than 40 are overstuffed.