Math / Data & Statistics

Questiond) equal to $1 / 10$ e) equal to $9 / 10$ because you were not caught in the last nine days.
3. A randomly selected student is asked to respond to wes, no or maxbe to the questions, "Do you intend to vote in the next presidential election?" The sample space is $\{Y, N, M a y b\}$ . Which of the following could be a legitimate assignment of probabilities for this sample space? a) $.4, .4, .4$ b) $.2, .6, .2$ c) $.3, .3, .3$ d) $.5, .4, .2$ e) $.1, .1, .1$
4. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would

Studdy Solution

STEP 1

1. The sample space is $\{Y, N, M\}$ , representing "Yes", "No", and "Maybe".
2. The sum of probabilities for all outcomes in a sample space must equal 1.
3. Each probability must be between 0 and 1, inclusive.

STEP 2

1. Evaluate each set of probabilities to ensure they sum to 1.
2. Check that each probability is between 0 and 1.

STEP 3

Evaluate option a) $.4, .4, .4$ :
$0.4 + 0.4 + 0.4 = 1.2$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 4

Evaluate option b) $.2, .6, .2$ :
$0.2 + 0.6 + 0.2 = 1.0$
The sum is equal to 1, so this is a legitimate probability assignment.

STEP 5

Evaluate option c) $.3, .3, .3$ :
$0.3 + 0.3 + 0.3 = 0.9$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 6

Evaluate option d) $.5, .4, .2$ :
$0.5 + 0.4 + 0.2 = 1.1$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 7

Evaluate option e) $.1, .1, .1$ :
$0.1 + 0.1 + 0.1 = 0.3$
Since the sum is not equal to 1, this is not a legitimate probability assignment.
The legitimate probability assignment is option b) $.2, .6, .2$ .

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Studdy Solution

STEP 1

1. The sample space is $\{Y, N, M\}$ , representing "Yes", "No", and "Maybe".
2. The sum of probabilities for all outcomes in a sample space must equal 1.
3. Each probability must be between 0 and 1, inclusive.

STEP 2

1. Evaluate each set of probabilities to ensure they sum to 1.
2. Check that each probability is between 0 and 1.

STEP 3

Evaluate option a) $.4, .4, .4$ :
$0.4 + 0.4 + 0.4 = 1.2$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 4

Evaluate option b) $.2, .6, .2$ :
$0.2 + 0.6 + 0.2 = 1.0$
The sum is equal to 1, so this is a legitimate probability assignment.

STEP 5

Evaluate option c) $.3, .3, .3$ :
$0.3 + 0.3 + 0.3 = 0.9$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 6

Evaluate option d) $.5, .4, .2$ :
$0.5 + 0.4 + 0.2 = 1.1$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 7

Evaluate option e) $.1, .1, .1$ :
$0.1 + 0.1 + 0.1 = 0.3$
Since the sum is not equal to 1, this is not a legitimate probability assignment.
The legitimate probability assignment is option b) $.2, .6, .2$ .

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Studdy Solution

STEP 1

1. The sample space is {Y,N,M}\{Y, N, M\}{Y,N,M}, representing "Yes", "No", and "Maybe".2. The sum of probabilities for all outcomes in a sample space must equal 1.3. Each probability must be between 0 and 1, inclusive.

STEP 2

1. Evaluate each set of probabilities to ensure they sum to 1.2. Check that each probability is between 0 and 1.

STEP 3

Evaluate option a) .4,.4,.4.4, .4, .4.4,.4,.4:0.4+0.4+0.4=1.2 0.4 + 0.4 + 0.4 = 1.2 0.4+0.4+0.4=1.2Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 4

Evaluate option b) .2,.6,.2.2, .6, .2.2,.6,.2:0.2+0.6+0.2=1.0 0.2 + 0.6 + 0.2 = 1.0 0.2+0.6+0.2=1.0The sum is equal to 1, so this is a legitimate probability assignment.

STEP 5

Evaluate option c) .3,.3,.3.3, .3, .3.3,.3,.3:0.3+0.3+0.3=0.9 0.3 + 0.3 + 0.3 = 0.9 0.3+0.3+0.3=0.9Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 6

Evaluate option d) .5,.4,.2.5, .4, .2.5,.4,.2:0.5+0.4+0.2=1.1 0.5 + 0.4 + 0.2 = 1.1 0.5+0.4+0.2=1.1Since the sum is not equal to 1, this is not a legitimate probability assignment.

STEP 7

Evaluate option e) .1,.1,.1.1, .1, .1.1,.1,.1:0.1+0.1+0.1=0.3 0.1 + 0.1 + 0.1 = 0.3 0.1+0.1+0.1=0.3Since the sum is not equal to 1, this is not a legitimate probability assignment. The legitimate probability assignment is option b) .2,.6,.2.2, .6, .2.2,.6,.2.

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1. The sample space is $\{Y, N, M\}$ , representing "Yes", "No", and "Maybe".
2. The sum of probabilities for all outcomes in a sample space must equal 1.
3. Each probability must be between 0 and 1, inclusive.

1. Evaluate each set of probabilities to ensure they sum to 1.
2. Check that each probability is between 0 and 1.

Evaluate option a) $.4, .4, .4$ :
$0.4 + 0.4 + 0.4 = 1.2$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

Evaluate option b) $.2, .6, .2$ :
$0.2 + 0.6 + 0.2 = 1.0$
The sum is equal to 1, so this is a legitimate probability assignment.

Evaluate option c) $.3, .3, .3$ :
$0.3 + 0.3 + 0.3 = 0.9$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

Evaluate option d) $.5, .4, .2$ :
$0.5 + 0.4 + 0.2 = 1.1$
Since the sum is not equal to 1, this is not a legitimate probability assignment.

Evaluate option e) $.1, .1, .1$ :
$0.1 + 0.1 + 0.1 = 0.3$
Since the sum is not equal to 1, this is not a legitimate probability assignment.
The legitimate probability assignment is option b) $.2, .6, .2$ .