Download 3. In an open refrigerator, there are seven different types of diet soda

3. In an open refrigerator, there are seven different types of diet soda, four different types of regular soda,
and two types of bottles of water.
a. Suppose Evan chose a bottle from the refrigerator at random. Could we realistically say that the
probability of choosing a diet soda is 7/13? Why or why not?
Yes, since there are 13 bottles and only 7 of them are diet, the probability of choosing a diet soda in a
random pick is 7/13.
b. If there are 16 total bottles of diet soda, 8 total bottles of regular soda, and 4 total bottles of water, what
is the probability of each of the following: (i) Choosing a bottle of diet soda when a bottle is chosen at
random (ii) Choosing a bottle of regular soda when a bottle is chosen at random (iii) Choosing a bottle of
water when a bottle is chosen at random
i) 2/3
ii) 1/3
iii) 1/6
6. List three real-world situations that do not involve weather or gambling where probability might be used.
1) A computer manufacturer estimating the probability a laptop will fail while under warranty
2) Evaluating results of DNA testing
3) Determining insurance rates from actuarial data
1. Suppose an experiment consists of spinning X and then spinning Y, as follows: Find the following:
(I’ll assume there are N numbers on the spinner, and all are equally likely.)
a. The sample space S for the experiment. 1/N2.
b. The event A consisting of outcomes from spinning an even number followed by an even number. 1/4
c. The event B consisting of outcomes from spinning at least one 2. 3/N2
d. The event C consisting of outcomes from spinning exactly one 2. 2/N2.
5. Following are two boxes containing colored and white balls. A ball is drawn at random from box 1. Then
a ball is drawn at random from box 2, and the colors of balls from both boxes are recorded in order. XXo
xoo Oo xxx 1 2 Find each of the following:
Assuming X means colored and O means white (case insensitive). Then Box 1 has three white and three
colored. Box 2 has two white and three colored.
a. The probability of two white balls
b. The probability of at least one colored ball
c. The probability of at most one colored ball
d. The probability of xo or ox
1/5
4/5
7/10
1/2
4. You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the
balls in the boxes in any way you like. You then are asked to select a box (after the boxes have been
shuffled) and to pick a ball at random from that box. If the ball is red, you win a prize. How should you
distribute the balls in the boxes to maximize your chances of winning? Justify your reasoning.
Put one white in the first box, and the remainder (two white and one red) in the other box. This gives you a
5/6 probability of obtaining a red ball on your pick. This is higher than any other possible configuration.
6. An estimate of the frog population in a certain pond was found by catching 30 frogs, marking them, and
returning them to the pond. The next day, 50 frogs were caught, of which 14 had been marked the previous
day. Estimate the frog population of the pond.
30/0.28 = 107 frogs
10. The following spinner is spun. Given the conditions listed below, what is the probability that out of 8, 2
is the answer.
We can’t really say from this information, but assuming there are 8 numbers, all equally likely, the
probability of getting a 2 is 1/8.
12. You play a game in which two dice are rolled. If a sum of 7 appears, you win $10; otherwise, you lose
$2.00. If you intend to play this game for a long time, should you expect to make money, lose money, or
come out about even? Explain.
P(7) = 1/6 so the winnings need to be 6 times the price to play or better. You would lose money on
average.
2. A game involves tossing two coins. A player wins $1.00 if both tosses result in heads. What should you
pay to play this game in order to make it a fair game? Explain your answer.
The probability of two heads is 1/4. At $0.25 per play, this would be a fair game.
3. Decide whether each of the following is true or false:
a. 6!/3=2!
false
b. 6!/5!=6!
false
c.6!/4!2!=15
true
d. n!(n+1)=(n+1)!
true
5. In a car race, there are 6 Chevrolets, 4 Fords, and 2 Pontiacs. In how many ways can the 12 cars finish if
we consider only the makes of the cars?
12! / (6! 4! 2!) = 13860
4. In how many ways can five couples be seated in a row of 10 chairs if no couple is separated? Explain
how you arrived at your answer.
10 chairs will seat exactly 5 couples, so this reduces to the number of permutations of 5 objects is 5! = 120.
5. a. Use the characteristics below in the Reasons for No Internet Access to draw a bar graph of the number
data. b. Describe how you handled the smaller number in your graph in relation to the much larger ones to
be depicted.
Total Characteristic Number in 1000s Percentage
INTERNET ACCESS
Total households 113,126 100.0
Internet access 61,852 54.7
No Internet access 51,274 45.3
REASONS FOR NO INTERNET ACCESS
Total households 51,274 100.0
Don’t need it, not interested 20,185 39.4
Costs are too high 11,950 23.3
No computer or computer inadequate 11,777 23.0
Lack of confidence or skills 2,282 4.5
Lack of time to use the Internet 1,177 2.3
Have access to Internet elsewhere 1,064 2.1
Concern that children will access inappropriate sites 451 0.9
Privacy and security concerns 402 0.8
Language barriers 266 0.5
Other reason 1,720 3.4 14.
Added data labels so small numbers would be readily available. An additional method for displaying data
with widely varying ranges is to use a logarithmic scale. However, this can convey a distorted sense of
quantity, so I opted not to use it here.
A list of presidents, with the number of children for each, follows:
1. Washington, 0
2. J. Adams, 5
3. Jefferson, 6
4. Madison, 0
5. Monroe, 2
6. J. Q. Adams, 4
7. Jackson, 0
8. Van Buren, 4
9. W. H. Harrison, 10
10. Tyler, 15
11. Polk, 0
12. Taylor, 6
13. Fillmore, 2
14. Pierce, 3
15. Buchanan, 0
16. Lincoln, 4
17. A. Johnson, 5
18. Grant, 4
19. Hayes, 8
20. Garfield, 7
21. Arthur, 3
22. Cleveland, 5
23. B. Harrison, 3
24. McKinley, 2
25. T. Roosevelt, 6
26. Taft, 3
27. Wilson, 3
28. Harding, 0
29. Coolidge, 2
30. Hoover, 2
31. F. D. Roosevelt, 6
32. Truman, 1
33. Eisenhower, 2
34. Kennedy, 4
35. L. B. Johnson, 2
36. Nixon, 2
37. Ford, 4
38. Carter, 4
39. Reagan, 4
40. G. Bush, 5
41. Clinton, 1
42. G. W. Bush, 2
a. Construct a dot plot for these data.
b. Make a frequency table for these data.
no. of
children
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
>15
c. What is the most frequent number of children?
9
no. of
presidents
6
2
9
5
8
4
4
1
1
0
1
0
0
0
0
1
0