math 182

MATH 182, MATHEMATICAL ANALYSIS II

Sample Final

1. In how many ways can 6 pictures be arranged on a wall if 3 are landscapes and 3 are portraits, and if

(a) like types must be kept together? (b) landscapes and portraits are alternated?

2. A student has 7 books on his desk.

(a) In how many ways can he select a group of 3?

(b) In how many ways can he select a group of 3 if a particular book must be selected?

3. A collection of golf balls contains 6 yellow, 2 blue, and 4 white balls. A golfer selects 4 balls at random. Find the probability that the selection includes the following.

(a) All white balls (b) 2 yellow and 2 white balls

(c) At least 1 blue ball (d) No white balls

4. Three cards are drawn at random from an ordinary deck of 52 cards. Find the probability that the 3-card hand contains the following:

(a) 2 kings (b) All clubs

(c) 3 cards of the same suit (d) At least 1 face card

5. Suppose that 5 percent of the clay planters fired in a certain way are defective. Assuming independence, find the probability of getting each result in a sample of 12 planters.

(a) 2 defective planters

(b) At most 2 defective planters

(c) At least 2 defective planters

6. The probability that a certain tennis player serves an ace is .25. Find the probabilities of the following results.

(a) He will serve exactly 2 aces out of 5 serves.

(b) He will serve at least 2 aces out of 5 serves.

(c) He will serve at most 2 aces out of 5 serves.

7. A die is rolled 6 times. Find the probability of rolling

(a) Exactly 3 ones (b) Exactly 2 ones (c) No more than 1 one

8. Two balls are drawn from a bag in which there are 3 green balls and 2 yellow balls. The number of green balls is counted.

(a) Find the probability distribution for the number of green balls.

(b) Find the expected number of green balls.

9. A coin is tossed 5 times and the number of heads is noted.

(a) Find the probability distribution for the number of heads.

(b) Find the expected number of heads.

10. Construct a bar chart

A random sample of skiers in Grand Junction last February counted 12 from Colorado, 27 from California, 19 from New York, 8 from Florida, and 6 from other states or nations.

11. Find the mode, median, and mean of each data set

(a) {10, 7, 9, 13, 11, 14, 15, 14, 8, 9}

(b) {11, 19, 20, 11, 12, 18, 11, 20, 16, 18, 17, 10, 13, 11, 15}

12. Find the sample standard deviation of each data set.

(a) {8, 13, 14, 17, 13}

(b) {18, 11, 18, 1, 5, 19}