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QuestionFind the probability that a randomly chosen prisoner takes no classes, given the prisoner counts: 449 (under 30) and 360 (30 and over). Round to three decimal places.

Studdy Solution

STEP 1

Assumptions1. The numbers in the table represent the number of prisoners in each category. These are all the prisoners we have3. We are looking for the probability that a randomly chosen prisoner does not take any classes

STEP 2

First, we need to find the total number of prisoners. We can do this by adding up all the numbers in the table.
Total prisoners=∑all categoriesNumber of prisonersTotal\, prisoners = \sum_{all\, categories} Number\, of\, prisoners

STEP 3

Now, plug in the given values from the table to calculate the total number of prisoners.
Total prisoners=58+108+449+24+37+360Total\, prisoners =58 +108 +449 +24 +37 +360

STEP 4

Calculate the total number of prisoners.
Total prisoners=58+108+449+24+37+360=1036Total\, prisoners =58 +108 +449 +24 +37 +360 =1036

STEP 5

Next, we need to find the number of prisoners who do not take any classes. This is given in the "Neither" column of the table.
Prisoners with neither classes=Number of prisoners in "Neither" columnPrisoners\, with\, neither\, classes = Number\, of\, prisoners\, in\, "Neither"\, column

STEP 6

Plug in the given values from the table to calculate the number of prisoners who do not take any classes.
Prisoners with neither classes=449+360Prisoners\, with\, neither\, classes =449 +360

STEP 7

Calculate the number of prisoners who do not take any classes.
Prisoners with neither classes=449+360=809Prisoners\, with\, neither\, classes =449 +360 =809

STEP 8

Now that we have the total number of prisoners and the number of prisoners who do not take any classes, we can calculate the probability that a randomly chosen prisoner does not take any classes. This is done by dividing the number of prisoners who do not take any classes by the total number of prisoners.
Probability=Prisoners with neither classesTotal prisonersProbability = \frac{Prisoners\, with\, neither\, classes}{Total\, prisoners}

STEP 9

Plug in the values for the number of prisoners who do not take any classes and the total number of prisoners to calculate the probability.
Probability=8091036Probability = \frac{809}{1036}

STEP 10

Calculate the probability and round the answer to at least three decimal places.
Probability=8091036≈0.781Probability = \frac{809}{1036} \approx0.781The probability that a randomly chosen prisoner does not take any classes is approximately0.781.

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