Question

1. Choose the two conditions that verify a table of relative frequencies is a probability model.

Select one or more:

a. The sum of the probabilities for all of the possible outcomes is less than 1.

b. The sum of the probabilities for all of the possible outcomes equals 1 (or 100%).

c. There is at least one zero probability for an event.

d. All of the probabilities for the possible outcomes are at least zero and no larger than 1.

2.

Look at the Table below for the probability events of pulling colored marbles from a bag. What do we call the event “orange”?

Color | Probability |
---|---|

Blue | 0.32 |

Red | 0.23 |

Orange | 0 |

Green | 0.17 |

Purple | 0.28 |

Select one:

a. Nothing

b. Certain.

c. Unusual.

d. Impossible.

3.

You have a coin and 4 marbles each a different color: Red, Blue, Green and Yellow. Consider the experiment of flipping a coin and pulling 1 marble from a bag and recording that combination as one outcome. What would be the sample space? Are all outcomes equally likely? Choose the correct answer below.

Use H, T for heads and the first letter for each color:
**R**ed, **B**lue, **G**reen
and **Y**ellow.

Select one:

a. S = { HR, HB, HG, HY, TR, TB, TG, TY }. Yes these are all equally likely outcomes.

b. S = { H, T, R, B, G, Y }. Yes these are all equally likely outcomes.

c. S = { H, T, R, B, G, Y }. No these are NOT equally likely outcomes.

d. S = { HR, HB, HG, HY, TR, TB, TG, TY }. No these are NOT equally likely outcomes.

4.

Use the Sample Space from problem #3 and find P(G) = Answer.

Enter your answer as a decimal rounded to 3 decimal places if necessary.

5.

Use the Sample Space from problem #3 and find P(T) = Answer.

Enter your answer as a decimal rounded to 3 decimal places if necessary.

6.

Use the Sample Space from problem #3 and find P(T or G) = Answer.

Enter your answer as a decimal rounded to 3 decimal places if necessary.

Answer #1

Que.1

The sum of the probabilities for all of the possible outcomes equals 1 (or 100%).

All of the probabilities for the possible outcomes are at least zero and no larger than 1.

Que.2

Impossible event.

Que.3

S = { HR, HB, HG, HY, TR, TB, TG, TY }. Yes these are all equally likely outcomes.

Que.4

G = {HG, TG}

Thus,

Que.5

T = { TR, TB, TG, TY }

Que.6

By addition theorem,

ALL of the following questions come from this problem: A Jar has
25 Red, 15 Blue, and 10 Green marbles in it. (denoted events R,B,G)
Calculate all to the following probabilities:
drawing three marbles all at once. Answer to at least 3 decimals
accuracy
1.) Probability none are red?
2.) Expected number of red marbles?
3.) Expected number of green marbles?

Suppose you roll, two
6-sided dice Write any probability as a decimal to three place
values and the odds using a colon. Determine the following:
1. The probability
that you roll a sum of seven (7)
2. The odds for
rolling a sum of four (4) is
3. The odds against
the numbers on both dice being the same is
Suppose you have a bag
with the following marbles: four (4) red, six (6) pink, two (2)
green, and seven...

You have seven green marbles, three red marbles, and two blue
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answer to 2 places after the decimal point. For example, an answer
of 0.7829 should be rounded to 0.78.)

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blue and one side painted yellow.
The die is rolled and the color of the
top side is recorded.
List all possible outcomes of this random experiment
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1. A particular slot machine in a casino has payouts set so that
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29%. Each game on the slot machine is independent of all other
games played on that machine. If a player chooses to play three
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she will win money in every one of those three games?
2. In a short string...

(i)State which method should be used to best determine the
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diagram.
(ii)Calculate the probability of the desired event (assuming all
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for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
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Observed Counts by Color...

Roulette USE SOFTWARE- In the
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red slots, and 2 green slots. In the game, a ball is rolled around
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Fair Table Probabilities
black
red
green
Probability
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19/40
2/40
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