Suppose 20% of babies born are born early, 50% are born on time, and 30% are born late. A nurse uses a random-number table to find the experimental probability that of 5 births, at least 1 baby will be born early. The digits 0 and 1 represent babies born early. The digits 2, 3, 4, 5, and 6 represent babies born on time. The digits 7, 8 and 9 represent babies born late.
23059 78234 01785 12359 26789
14568 24579 13579 01239 24589
03489 12456 01458 23567 01238
01235 34567 23478 13546 23589
Find the experimental probability that of 5 babies born, at least 1 will be born early.
A. start fraction 1 over 5 end fraction
B. The fraction is 2 over 5.
C. three-fifths
D. four-fifths
How many different arrangements can be made with the letters from the word SPACE?
A. 24
B. 32
C. 60
D. 120
Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
A. 21
B. 108
C. 220
D. 306
Write the number of permutations in factorial form. Then simplify.
How many different ways can you and five friends sit in your assigned seats when you go to a concert?
A. 6!; 120
B. 6!; 720
C. 5!; 120
D. 5!; 30
Below are the results of tossing a number cube 7 times. Find the experimental probability of tossing an even number.
6 4 3 2 5 3 3
A. start fraction 3 over 7 end fraction
B. start fraction 2 over 7 end fraction
C. one-half
D. start fraction 4 over 7 end fraction
How many different ways can the students at a school select the president, vice president, and secretary from a group of 5 people?
A. 120
B. 60
C. 20
D. 15
When buying a new car, you have a choice of 4 different models, 3 different colors, and 2 different sizes. How many choices are there for one car?
A. 5
B. 12
C. 16
D. 24
There are 25 people competing in a race. In how many ways can they finish in first and second place?
A. 49
B. 400
C. 600
D. 625
A bag contains tiles with the letters C-O-M-B-I-N-A-T-I-O-N-S. Lee chooses a tile without looking and doesn’t replace it. He chooses a second tile without looking. What is the probability that he will choose the letter O both times?
A. 1 over 132
B. start fraction 1 over 72 end fraction
C. 1 over 66
D. 1 over 23Start Fraction 1 over 23 End Fraction
A sandwich shop offers the following toppings. How many two-topping sandwiches can you make?
lettuce
tomato
bacon
cheese
mustard
A. 8
B. 10
C. 12
D. 20
Answers:
1. B. The fraction is 2 over 5.
2. C. 60
3. C. 220
4. B. 6!; 720
5. B. start fraction 2 over 7 end fraction
6. A. 120
7. D. 24
8. D. 625
9. B. start fraction 1 over 72 end fraction
10. C. 12
1. Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled from 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain.
2. A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
What is the probability of selecting a purple marble and then a white marble?
What is the probability of selecting two white marbles?
Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.
1. Hallie should roll two number cubes. The probability of getting a 5 on one spin of the wheel is 1/6. The probability of rolling the same number on both number cubes is also 1/6 (1/6 for getting a specific number on the first cube multiplied by 1/6 for getting the same number on the second cube). However, Hallie has two chances to get a match with the number cubes, whereas she only has one chance with the wheel. Therefore, rolling two number cubes gives Hallie a higher probability of winning the grand prize.
2.
- The probability of selecting a purple marble first is 7/9. After removing one marble, there will be 8 marbles left in the bag, including one white marble. Therefore, the probability of selecting a white marble second is 1/8. The overall probability is (7/9) x (1/8) = 7/72.
- The probability of selecting a white marble first is 2/9. After removing one marble, there will be 8 marbles left in the bag, including one white marble. Therefore, the probability of selecting another white marble is 1/8. The overall probability is (2/9) x (1/8) = 1/36.
- There is a greater chance of selecting two purple marbles in a row. The probability of selecting a purple marble first is 7/9. After removing one marble, there will be 8 marbles left in the bag, including 6 purple marbles. Therefore, the probability of selecting another purple marble is 6/8, which simplifies to 3/4. The overall probability is (7/9) x (3/4) = 21/36. This probability is greater than the probability of selecting two white marbles in a row (1/36).