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reduced fraction form

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1. A bag contains 6 purple marbles, 7 azure marbles and 10 orange marbles. What is the chance of drawing a purple marble? If a 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.

2. A mini license plate for a toy car must consist of a one digit odd number followed by two letters. Each letter must be a J or K. Repetition of letters is permitted.
* Use the counting principle to determine the number of points in the sample space.
* Construct a tree diagram to represent this situation.
* List the sample space.
* Determine the exact probability of creating a mini license plate with a J. Give solution exactly in reduced fraction form.

3. A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

* a three, given the card is a not a face card.
* a four, given the card is not a diamond.
* a Jack given the card is not a face card.

Show step by step work. Give all solutions exactly in reduced fraction form.

4. A bag contains a total of 20 batteries, of which four are defective. Selecting two at random, without replacement, determine the probability that none of the batteries you select are good.

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Solution Summary

This solution uses the counting principle to determine the number of points in the sample space.

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Statistics: 9 Probability questions

See attached file.

1. At a swimming pool there are 2 managers, 8 lifeguards, 3 concession stand clerks, and 2 maintenance people. If a person is selected at random, find the probability that the person is either a lifeguard or a manager.

2. An automobile dealer has 10 Fords, 7 Buicks, and 5 Plymouths on his used-car lot. If a person purchases a used car, find the probability that it is a Ford or a Buick. Answer should be in fraction.

3. In a meeting there are five women and four men. If one person is selected, find the probability that the person is a woman

4. The following data were obtained in response to the question, "Do you favor the proposal of the school's combining the elementary and middle school students in one building?"

Gender Yes No No Opinion
Males 72 81 5
Females 103 68 7

If a person is selected at random, what is the probability the person is a male or is against the issue?

5. Please put your answer in fraction form fully reduced.
The following data were obtained in response to the question, "Do you favor the proposal of the school's combining the elementary and middle school students in one building?"

Gender Yes No No Opinion
Males 72 81 5
Females 103 68 7

If a person is selected at random, what is the probability that the person is a female or favors the issue?

6. Some graduates' average grades and degrees showed the following results.

Degree C B A
B.S. 5 8 15
B.A. 7 12 8

If a graduate is selected at random, find this probability:
The graduate has a B.S. degree, given that he or she has an A average.
Please put your answer in reduced fraction form

7. Some graduates' average grades and degrees showed the following results.

Degree C B A
B.S. 5 8 15
B.A. 7 12 8

If a graduate is selected at random, find this probability:
Given that the graduate has a B.A. degree, the graduate has a C average.
Please put your answer in reduced fraction form

8. There are five Biology instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor.
Please answer in reduced fraction form

9. A van contains three kindergartners and five first-graders. If two children are ill, find the probability that at least one of them is a kindergartner.
Please answer in reduced fraction form

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