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QuestionFind the numbers for a Venn diagram where P(A∣B)=515P(A|B) = \frac{5}{15}, given 25 regular exercisers and 15 dieters.

Studdy Solution

STEP 1

Assumptions1. The total number of people trying to lose weight is the sum of the people who exercise regularly and the people who are on a diet. . Event A represents the people who exercise regularly.
3. Event B represents the people who are on a diet.
4. The probability that a person who is trying to lose weight exercises regularly, given that they are also on a diet is 515\frac{5}{15}.

STEP 2

First, we need to find the number of people who exercise regularly and are also on a diet. This can be found by multiplying the total number of people who are on a diet by the given probability.
Number of people who exercise and diet=Total number of people on a diettimesProbabilityNumber\, of\, people\, who\, exercise\, and\, diet = Total\, number\, of\, people\, on\, a\, diet \\times Probability

STEP 3

Now, plug in the given values for the total number of people on a diet and the probability to calculate the number of people who exercise and diet.
Number of people who exercise and diet=15times515Number\, of\, people\, who\, exercise\, and\, diet =15 \\times \frac{5}{15}

STEP 4

Calculate the number of people who exercise and diet.
Number of people who exercise and diet=15times15=Number\, of\, people\, who\, exercise\, and\, diet =15 \\times \frac{}{15} =

STEP 5

Now that we have the number of people who exercise and diet, we can find the number of people who only exercise or only diet.For people who only exercise, subtract the number of people who exercise and diet from the total number of people who exercise.
Number of people who only exercise=Total number of people who exercise−Number of people who exercise and dietNumber\, of\, people\, who\, only\, exercise = Total\, number\, of\, people\, who\, exercise - Number\, of\, people\, who\, exercise\, and\, diet

STEP 6

Plug in the values for the total number of people who exercise and the number of people who exercise and diet to calculate the number of people who only exercise.
Number of people who only exercise=25−5Number\, of\, people\, who\, only\, exercise =25 -5

STEP 7

Calculate the number of people who only exercise.
Number of people who only exercise=25−5=20Number\, of\, people\, who\, only\, exercise =25 -5 =20

STEP 8

For people who only diet, subtract the number of people who exercise and diet from the total number of people who diet.
Number of people who only diet=Total number of people who diet−Number of people who exercise and dietNumber\, of\, people\, who\, only\, diet = Total\, number\, of\, people\, who\, diet - Number\, of\, people\, who\, exercise\, and\, diet

STEP 9

Plug in the values for the total number of people who diet and the number of people who exercise and diet to calculate the number of people who only diet.
Number of people who only diet=15−5Number\, of\, people\, who\, only\, diet =15 -5

STEP 10

Calculate the number of people who only diet.
Number of people who only diet=15−5=10Number\, of\, people\, who\, only\, diet =15 -5 =10So, in the Venn diagram, the number of people who only exercise is20, the number of people who only diet is10, and the number of people who do both is5.

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