Probability Practice Additional Problems

Probability Practice – Additional Problems

1. The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?

2. The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&Ms, red another 20%, and orange, blue and green each made up 10%. The rest were brown. a) if you pick an M&M at random, what is the probability that 1. it is brown 2. it is yellow or orange 3. it is not green 4. it is striped b) if you pick three M&Ms in a row, what is the probability that 1. they are all brown 2. the third one is the first one that is red 3. none are yellow 4. at least one is green

3. In #2 you calculated the probabilities of getting various M&Ms. Some of your answers depended on the assumption that the outcomes described were disjoint, and some answers depended on the assumption that the events were independent. a) If you draw one M&M, are the vents of getting a red one and getting an orange one disjoint or independent or neither? b) If you draw two M&Ms one after the other, are the vents of getting a red on the first and a red on the second disjoint or independent or neither? c) can disjoint events ever be independent?

4. You roll a fair die three times. What is the probability that a) you roll all 6’s b) you roll all odd #’s c) non of you rolls gets a number divisible by 3 d) you roll at least one 5 e) the numbers you roll are not all 5’s

5. A certain bowler can bowl a strike 70% of the time. What is the probability that she a) goes three consecutive frames without a strike b) makes her first strike in the third frame? c) has a least one strike in the first three frames? d) bowls a perfect game? (12 consecutive strikes)

6. You bought a new set of four tires from a manufacturer who just announced a recall because 2% of those tires are defective. What is the probability that at least one of yours is defective?

7. For each of the following list the sample space and tell whether you think the events are equally likely. a) Toss 2 coins, record the order of heads and tails b) A family has 3 children, record the # of boys c) flip a coin until you get a head or 3 consecutive tails d) Roll two dice, record the larger #

8. A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs and 21% had both a TV and a refrigerator. What’s the probability that a randomly selected dorm room has a) a TV but no refrigerator b) a TV or a refrigerator, but not both? c) neither a TV or a refrigerator

9. You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities a) the card is a heart, given that it is red b) the card is red, given that it is a heart c) the card is an ace, given that it is red d) the card is a queen, given that it is a face card

10. Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat?

11. Leah is flying from Boston to Denver with a connection in Chicago. The probability that her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95 but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) are the first flight leaving on time and the luggage making the connection independent events? Explain b) What is the probability that her luggage arrives in Denver with her? c) Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that Leah’s first flight was delayed?

12. Dan’s diner employs three dishwashers. Al washes dishes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but chuck breaks 3% of the dishes he washers. You go to Dan’s for supper one night and hear a dish break at the sink. What’s the probability that Chuck broke the dish?

13. A chest of drawers contains three identical drawers. One drawer contains three gold coins, another contains two gold coins and two silver coins, and another contains one gold and two silver coins. A drawer is chosen at random, and a coin from the drawer is chosen at random. What is the probability that the coin chosen is gold?

14. Same chest, same three identical drawers. Now, one drawer contains two gold coins, and each of the other two drawers contains one gold coin and one silver coin. A drawer is chosen at random, and a coin from that drawer is chosen at random. If a gold coin is chosen, that is the probability that the other coin in the drawer is also gold?

15. If a person is vaccinated properly, the probability of his or her getting a certain disease (statistiosis) is .05. Without vaccination, the probability of getting statistiosis is .35. Assume 1/3 of the population is properly vaccinated. a) if a person is randomly selected from the population what is the probability of that person’s getting the disease? b) If a person gets statistiosis, what is the probability that he or she was vaccinated?

16. If P(A) = 0.4 and P(B) = 0.5, and P(A and B) = 0.1, find P(A or B)

17. Suppose that P(A) = 0.3, P(B) = 0.4 and P(A and B) = 0.12 a) find P(B|A) b) find P(A|B) c) Are A and B independent?

18. Two flower seeds are randomly selected from a package that contains 5 seeds for red flowers, and 3 seeds for white flowers. a. what is the probability that both seeds will result in red flowers? b. what is the probability that one of each color is selected? c. what is the probability that both seeds are white flowers? d. what is the probability that at least one seed will produce a red flower?

19. In an article titled “Why Quitting Means Gaining” (Time, March 25, 1991), it was reported that giving up cigarette smoking often results in gaining weight. In examining a group of quitters, the following data were found: Weight Gain Major Significant Moderate Slight Men .09 .14 .22 .55 Women .12 .11 .16 .50

* Due to rounding, numbers for women do not add to 100%

Suppose that 60% of the group were men and 40% were women. If a participant were randomly selected and found to have experienced a) a major weight gain, find the probability that it was a male b) a slight weight gain, find the probability that it was a woman.