2. Two cards are selected in sequence from a standard deck. Find the probability that the second card is a queen given that the first card is a king. Assume that the king is not replaced. answer = 4/51
3. A box contains 10 red balls, 8 yellow balls and 3 green balls. If two balls are drawn in succession without replacement, find the probability of getting a green ball on the second draw given that a red ball was drawn on the first draw P(G|R) answer = 3/20
4.In a box of 11 parts, four are defective. Two parts are drawn in succession without replacement. Find the probability that the second part is defective given that the first part was defective. answer = .3
1.If the odds of an event occurring are 5 to 4, find the probability that the event will not occur. answer = 4/9
2. If the probability of an event occurring is 2/5, find the odds against the event occurring. answer = 3/2
Compound Probabilities
1.A card is drawn from a standard deck. Find the probability that the card is an ace or a four. answer =.154
2.A die is tossed. Find the probability that the number is less than three or an odd number. answer= 0.667
3.Using the table below, find the probability that a blood donor has type A or type O blood. answer =.851
4. Find the probability that a donor has type B blood or is RH negative. answer = .249
| Type O | Type A | Type B | Type AB | Total | |
| RH Positive | 156 | 139 | 37 | 12 | 344 |
| Rh Negative | 28 | 25 | 8 | 4 | 65 |
| 184 | 164 | 45 | 16 | 409 |
5. Two cards are selected in succession without replacement. Find the probability of selecting a King and then selecting a Queen. answer = 0.006
6.A coin is tossed and a die is tossed. Find the probability of getting a head and a two. answer = 0.083
7.The probability that a fish swims successfully swims a dam is 0.85. Find the probability that three fish swim successfully swim the dam. answer = 0.614
8. Find the probability that none of the fish successfully swims the dam. answer = 0.003
9. Find the probability that at least one of the fish successfully swims the dam. Hint use the idea P(~A) = 1 - P(A) answer = 0.997
1.You are purchasing a new car. You can choose from Ford, GM, Chrysler, you can select a mid-size or full-sized automobile, you can select red, white, black or green. How many different ways can you select a car of one manufacturer, one size and color? answer = 24
2. The access code for a car's security system consists of four digits. Each digit can be o through 9. How many access codes are possible if
(a) each digit can be used only once? answer = 5040
(b) each digit can be repeated? answer = 10,000
(c) each digit can be repeated only once. answer =7,290
1.A company plans to develop a new system of interstate highways and receives 16 bids for the project. The company plans to hire four of the bidding companies. How many different combinations of four companies can be selected from the 16 bidding companies? answer = 1820
2. A committee of 5 math students, 4 English students and 6 History students are to be selected from 10 math students, 8 English students and 9 History students. In how many was can this be accomplished? answer = 1,481,760
3.Twenty five books are to be placed in bins. Twelve of the books go in the red bin, then 10 books go in the blue bin and the remaining books go in the green bin. In how many ways can this be accomplished? answer = 1,487,285,800
4. In how many ways can 5 cards be drawn from a deck of 52 cards? answer= 2,598,960
1.The starting lineup for a baseball team consist of nine players. How many different batting orders are possible using the nine players? answer =362,880
2.Forty-three race cars started the 2004 Daytona 500. How many ways can the cars finish first, second, and third? answer = 74,046
3.The board of directors of a college has 12 members. One member can be selected president, another can be selected vice president and another can be selected secretary. How many ways can these positions be assigned? answer = 1,320
4.In how many ways van 7 people be seated in a line if two people insist upon being seated together? answer = 1,440
5. In how many ways can 7 people be seated in a line if two people will not be seated next to each other? answer 3,600
A company that has 25 employees chooses a committee of 6 to represent employees at a general meeting. When the committee was formed, none of the 10 minority employees were selected.
(a) In how many ways can 6 employees be selected from 25 employees? answer =177,100
(b) In how many ways can 6 employees be selected from 15 employees? answer = 5005
(c) If the committee of 6 was chosen randomly ( without bias), what is the probability that it contained no minorities? answer = .028
(d) Does your answer to part (c) indicate that the committee selection was biased?
answer = probably, since the probability of selecting no minorities in an unbiased sample occurs about 28 times in every1000 samples