Question

Compute each of the following probabilities. Label each problem clearly and show all your work. Use the numbers you computed in earlier parts of the project based on the class data set.

- Problem 1: Suppose all of the Skittles in the class data set
are combined into one large bowl and you are going to randomly
select one Skittle.
- (a) What is the probability that you select a green Skittle? (4 points)
- (b) What is the probability that you select a Skittle that is NOT green? (4 points)
- (c) What is the probability that you select a Skittle that is red OR yellow? (4 points)
- (d) What is the probability that you select a Skittle that is orange GIVEN that it is a secondary color (secondary colors are green, orange and purple)? (4 points)

- Problem 2: Suppose you are going to randomly select two
Skittles from the bag YOU purchased.
- (a) What is the probability that both Skittles are purple if you select them with replacement? Give your answer correct to four decimal places. (4 points)
- (b) What is the probability that both Skittles are purple if you select them without replacement? Give your answer correct to four decimal places. (4 points)
- (c) What is the probability that the first skittle is purple and the second skittle is not purple if you select them with replacement? (4 points)
- (d) What is the probability that at least one Skittle is purple if you select them with replacement? (4 points)

- Problem 3: Suppose all of the Skittles in the class data set
are combined into one large bowl and you are going to randomly
select ten Skittles with replacement and count how many are yellow.
- (a) List the requirements of the binomial probability distribution and show that this meets them, including identifying the values for n and p. (6 points)
- (b) What is the probability that exactly 4 of the 10 Skittles are yellow? (4 points)
- (c) What is the probability that at most 2 of the 10 Skittles are yellow? (4 points)
- (d) For samples of size 10, what is the expected value and standard deviation for the number of yellow skittles that will be included? (4 points)

Red | Orange | Yellow | Green | Purple | Total | Height |

5 | 6 | 8 | 12 | 15 | 46 | 65 |

11 | 10 | 8 | 14 | 8 | 51 | 70 |

10 | 12 | 7 | 13 | 12 | 54 | 63 |

17 | 14 | 3 | 21 | 0 | 55 | 63.5 |

10 | 11 | 9 | 13 | 13 | 56 | 71 |

13 | 11 | 11 | 14 | 7 | 56 | 71 |

16 | 9 | 8 | 11 | 12 | 56 | 73.5 |

19 | 8 | 14 | 8 | 8 | 57 | 62 |

14 | 14 | 11 | 9 | 9 | 57 | 62 |

15 | 9 | 13 | 11 | 9 | 57 | 61 |

12 | 12 | 12 | 15 | 6 | 57 | 66 |

13 | 15 | 13 | 6 | 10 | 57 | 62 |

10 | 10 | 11 | 15 | 11 | 57 | 76 |

10 | 13 | 16 | 10 | 8 | 57 | 60 |

11 | 10 | 15 | 9 | 13 | 58 | 72 |

11 | 15 | 10 | 11 | 11 | 58 | 61 |

12 | 12 | 13 | 9 | 12 | 58 | 68 |

7 | 17 | 13 | 11 | 10 | 58 | 66 |

20 | 13 | 7 | 10 | 8 | 58 | 67 |

11 | 14 | 10 | 11 | 12 | 58 | 65 |

9 | 12 | 13 | 11 | 13 | 58 | 68 |

10 | 14 | 8 | 15 | 11 | 58 | 69 |

9 | 12 | 10 | 12 | 15 | 58 | 69 |

13 | 15 | 12 | 12 | 6 | 58 | 62 |

10 | 11 | 13 | 12 | 12 | 58 | 62 |

13 | 15 | 14 | 9 | 7 | 58 | 67 |

19 | 8 | 12 | 8 | 11 | 58 | 63.6 |

15 | 13 | 12 | 9 | 10 | 59 | 62 |

10 | 13 | 16 | 6 | 14 | 59 | 74 |

4 | 11 | 12 | 14 | 18 | 59 | 68 |

15 | 15 | 11 | 11 | 7 | 59 | 68 |

14 | 10 | 10 | 11 | 14 | 59 | 74 |

6 | 15 | 12 | 11 | 15 | 59 | 58 |

13 | 15 | 10 | 13 | 8 | 59 | 67.2 |

15 | 10 | 11 | 13 | 10 | 59 | 63 |

7 | 11 | 20 | 11 | 10 | 59 | 64 |

11 | 11 | 9 | 13 | 15 | 59 | 62 |

12 | 11 | 14 | 11 | 11 | 59 | 61 |

14 | 10 | 14 | 8 | 13 | 59 | 64 |

10 | 15 | 12 | 9 | 13 | 59 | 66 |

12 | 13 | 12 | 8 | 14 | 59 | 62 |

11 | 8 | 16 | 12 | 12 | 59 | 62.4 |

7 | 14 | 7 | 16 | 15 | 59 | 66 |

7 | 17 | 17 | 10 | 8 | 59 | 66 |

14 | 10 | 9 | 14 | 12 | 59 | 61 |

11 | 14 | 13 | 12 | 9 | 59 | 65 |

13 | 10 | 7 | 15 | 14 | 59 | 67 |

14 | 10 | 14 | 14 | 7 | 59 | 68 |

9 | 16 | 13 | 10 | 12 | 60 | 61.5 |

8 | 12 | 9 | 13 | 18 | 60 | 62 |

13 | 11 | 4 | 18 | 14 | 60 | 62 |

4 | 15 | 10 | 18 | 13 | 60 | 63 |

8 | 20 | 12 | 12 | 8 | 60 | 63 |

13 | 14 | 14 | 11 | 8 | 60 | 62.5 |

14 | 12 | 11 | 13 | 10 | 60 | 60 |

13 | 18 | 7 | 13 | 9 | 60 | 63 |

11 | 15 | 12 | 12 | 10 | 60 | 61 |

20 | 14 | 7 | 9 | 10 | 60 | 70 |

10 | 17 | 14 | 11 | 8 | 60 | 61 |

24 | 6 | 8 | 11 | 11 | 60 | 67 |

12 | 13 | 11 | 9 | 15 | 60 | 62.4 |

11 | 13 | 10 | 16 | 10 | 60 | 63 |

12 | 12 | 12 | 10 | 14 | 60 | 69 |

10 | 13 | 11 | 18 | 9 | 61 | 60 |

18 | 9 | 11 | 9 | 14 | 61 | 66 |

11 | 13 | 8 | 11 | 18 | 61 | 70 |

9 | 11 | 9 | 20 | 12 | 61 | 62 |

14 | 16 | 13 | 8 | 10 | 61 | 67.5 |

13 | 12 | 13 | 11 | 12 | 61 | 69 |

16 | 11 | 8 | 11 | 15 | 61 | 72 |

8 | 10 | 24 | 5 | 14 | 61 | 66 |

9 | 12 | 11 | 15 | 14 | 61 | 61.5 |

13 | 18 | 11 | 10 | 9 | 61 | 70 |

15 | 11 | 8 | 14 | 13 | 61 | 68 |

12 | 14 | 9 | 11 | 15 | 61 | 72 |

11 | 21 | 9 | 8 | 13 | 62 | 65 |

20 | 7 | 9 | 19 | 7 | 62 | 60 |

10 | 12 | 10 | 15 | 15 | 62 | 66 |

16 | 14 | 12 | 12 | 8 | 62 | 65 |

16 | 13 | 10 | 14 | 9 | 62 | 66 |

12 | 13 | 16 | 13 | 8 | 62 | 62 |

14 | 7 | 13 | 12 | 16 | 62 | 69 |

8 | 12 | 14 | 17 | 12 | 63 | 69 |

14 | 11 | 11 | 12 | 16 | 64 | 68 |

12 | 9 | 12 | 17 | 14 | 64 | 62 |

18 | 11 | 19 | 8 | 8 | 64 | 61 |

Answer #1

1)

Red | Orange | Yellow | Green | Purple | Total |

1046 | 1066 | 977 | 1029 | 969 | 5087 |

(a) What is the probability that you select a green Skittle? (4 points)

= 1029/5087

= 0.20228

(b) What is the probability that you select a Skittle that is NOT green? (4 points)

= 1 - 0.20228

= 0.79772

(c) What is the probability that you select a Skittle that is red OR yellow? (4 points)

(1046 + 977)/5087

= 0.39768

(d) What is the probability that you select a Skittle that is orange GIVEN that it is a secondary color (secondary colors are green, orange and purple)? (4 points)

=1066/(1066 + 1029 + 969)

= 0.347911

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Skittles in a package? Use the attached Skittles sample and test at
the significance level of .01
Package
Red
Orange
Yellow
Green
Purple
Total
Dominant Color
1
15
15
16
12
14
72
Y
2
13
6
11
16
15
61
G
3
9
9
10
18
15
61
G
4
7
9
8
18
15
57
G...

Bag
Blue
Orange
Green
Yellow
Red
Brown
Total Number of Candies
1
7
23
9
11
4
6
60
2
16
16
4
7
9
4
56
3
14
14
3
10
5
11
57
4
13
14
7
8
8
6
56
5
18
12
7
10
5
7
59
6
12
9
11
9
8
8
57
7
15
16
6
6
6
8
57
8
15
17
8
4
6
7
57
9
12
14
10
5...

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1
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x
y
1
12
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