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# sets and probability of marble drawn from a box

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28. A marble is drawn from a box containing 3 yellow, 4 white, and 8 blue marbles. Find
the odds in favor of drawing the following.
a. A yellow marble b. A blue marble c. A white marble

If two cards are drawn without replacement from an ordinary deck, find the probabilities
of the following results

8. The second is black, given that the first is a spade.

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#### Solution Preview

28. You can see that you have 15 marbles in total.

a. yellow = 3/15 = 1/5
b. blue = 8/15
c. white = 4/15

8. I assume ...

#### Solution Summary

This solution goes over probability with regards to marbles drawn from a box.

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## theoretical probability

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2. A bag contains 16 yellow marbles, 6 green marbles, and 7 red marbles. What is the chance of drawing a yellow marble? If a yellow marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a green marble? Give solutions exactly in reduced fraction form, separated by a comma.

3. The odds in favor of Sprinting Sarah winning the horse race are 19:3. Determine the probability that Sprinting Sarah wins the horse race.
3/19
22/3
3/22
19/22
19/3

4. The odds against Trotting Carlos winning the horse race are 29:7. Determine the probability that Trotting Carlos wins the horse race.
7/29
36/7
29/36
29/7
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5. A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.

1. Use the counting principle to determine the number of points in the sample space.
2. Construct a tree diagram to represent this situation List the sample space.
3. List the sample space.
4. Determine the exact probability of creating a mini license plate with a 7. Give solution exactly in reduced fraction form

6. Suppose 42 newly created pairs of jeans are placed in a bin to be checked for quality. Of these, 4 will not be of high enough quality to sell. Suppose that two pairs of jeans are randomly selected, without replacement, from the bin. What is the chance that both pairs of jeans selected will be substandard? Show step by step work! Give solution as a reduced fraction in lowest terms and approximated to the nearest ten thousandth.

7. The FM Radio stations with high signal strength in New Orleans break down into the following categories:
Hip hop 2
Religious 6
Country 2
Rock 3
Other 5

If someone driving in New Orleans tuned into an FM radio station with high signal strength at random, what would be the chances he would not get a Country station? Give answer as a fraction in lowest terms.

8. The pets a particular veterinarian saw yesterday break down into the following categories:
Cats 10
Dogs 18
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If there is one folder per pet and Valerie selected a folder at random from yesterday's stack of folders, what would be the chances she would not get a bird's chart? Give answer as a fraction in lowest terms
9. If casino Keno were fair, how much should it pay to a player who bets \$10 to bet 6 numbers and matches 5 numbers? The odds against matching 5 numbers when you bet 6 numbers in casino Keno are about 322 to 1.

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2. A bag contains 6 purple marbles, 7 azure marbles and 10 orange marbles. What is the chance of drawing a purple marble? If an purple marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing an orange marble? Give solutions exactly in reduced fraction form, separated by a comma

3. A boxed DVD set contains 18 movies from a certain studio. Ten of them are comedies, five are thrillers, and three are dramas. What is the probability that one DVD chosen from the box at random is a thriller or a comedy? Show step by step work! Give answer as a fraction in lowest terms.

4. According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

State 2008 Population
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Pennsylvania 12,448,279
Tennessee 6,214,888
Utah 2,736,424
Washington 6,549,224

SOURCE: U. S. Census Bureau

What is the probability that a randomly selected U.S. resident did not live in Utah? Show step by step work. Round solution to the nearest thousandth.

5 .
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1. Use the counting principle to determine the number of points in the sample space.
2. Construct a tree diagram to represent this situation
3. List the sample space.
4. Determine the exact probability of creating a mini license plate with an R. Give solution exactly in reduced fraction form.

6. A parent can choose from 7 types of protein, 4 vegetables and 5 desserts. If the parent serves a meal of 1 protein, 1 vegetable and 1 dessert to the family, how many different meals can be served?

7. A card is selected from a standard deck of 52 playing cards. Find the probability of selecting

1. a prime number under 10 given the card is red. (1 is not prime.)
2. a King, given that the card is not a heart.
3. a nine given the card is a face card. (An ace is not a face card.)

Please show step by step work. Give all solutions exactly in reduced fraction form.
8. Last fall, a gardener planted 55 iris bulbs. She found that only 45 of the bulbs bloomed in the spring.

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9. In how many ways can 8 instructors be assigned to five sections of a course in mathematics?

10.
Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.

A. drawing a black seven out of a standard 52 card deck given it's not a face card or an ace.
B. rolling a total of 4 on two fair six sided dice
C. drawing a three out of a standard 52 card deck given it's not a face card or an ace.
D. rolling a total of 9 on two fair six sided dice
E. rolling a total of 7 on two fair six sided dice

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12. How many different ways are there for an admissions officer to select a group of 5 college candidates from a group of 9 applicants for an interview?

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