1. Blood comes in four types: O, A, B, and AB. The percentages of people in the United States with each blood type are shown below.
- Draw out the sample space for two people getting married with all the different combinations of blood types. Assume the two persons are independent. (Hint: The sum of the probabilities must equal 1.00.)
- What is the probability that two people getting married both have blood type O?
- What is the probability that two people getting married both have the same blood type?
- Do you think that the assumption of independence is reasonable for blood type for a couple
2. A card is drawn at random from a standard 52-card deck. A deck of cards has 52 cards and four suits (hearts, diamonds, spades, and clubs).There are 13 cards in each suit (1–10, jack, queen, and king; the last three are considered face cards). Answer the following probabilities:
- The probability the card is a heart
- The probability the card is a heart or a 2
- The probability the card is black face and a face card
3. Joanna takes a multiple-choice quiz of four questions that is administered on a clicker in class. Each question has four possible answers (three wrong, one right). Assume the questions are independent of each other.
- Draw out the sample space for the four questions using R to stand for Right and W to stand for Wrong.
- What is the probability that she answers only one question correctly?
- What is the probability that she gets all four questions right?
- What is the probability that she gets all four questions wrong?
- What is the probability that she gets at least two questions right?
- What is the probability that she gets at least one question right?
4. For high school students, admission to the nation’s most selective universities is very competitive. For example, it was reported in 2007 that elite school A accepted about 12% (0.12) of its applicants, and elite school B accepted 18% (0.18). Joanna has applied to both schools. Assuming she is a typical applicant, she figures her chances of getting into both A and B must be about 2.16% (0.0216).
- How did she arrive at this conclusion?
- What additional assumption is she making?
- Do you agree with her conclusion?
- Suppose the conditional probability of getting into B, given you are already accepted into A, is 0.82. Now what is the probability of getting into both A and B?
5. A telemarketer who needs to make many phone calls has estimated that when he calls a prospective client, the probability that he will reach the client right away is 0.5. If he does not reach the client on the first call, the probability that he will reach the client on a subsequent call in the next half-hour is 0.15.
- What’s the probability that the telemarketer will reach his client on the second call, but not on the first call?
- What’s the probability that the telemarketer will be unsuccessful on two consecutive calls?
- What’s the probability that the telemarketer will reach his client in two or fewer calls?