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QuestionFind the numbers for women working full-time and having children in a Venn diagram, given P(A∣B)=527P(A|B) = \frac{5}{27}.

Studdy Solution

STEP 1

Assumptions1. The probability that a woman works full-time, given that she has children is 527\frac{5}{27}. . There are30 women who work full-time.
3. There are27 women who have children.
4. Event AA represents working full-time, and Event BB represents having children.

STEP 2

First, we need to find the number of women who work full-time and have children. This is given by the conditional probability of a woman working full-time given that she has children.
(A∣B)=Number of women who work full−time and have childrenNumber of women who have children(A|B) = \frac{Number\, of\, women\, who\, work\, full-time\, and\, have\, children}{Number\, of\, women\, who\, have\, children}

STEP 3

Now, plug in the given values for the probability and the number of women who have children to calculate the number of women who work full-time and have children.
527=Number of women who work full−time and have children27\frac{5}{27} = \frac{Number\, of\, women\, who\, work\, full-time\, and\, have\, children}{27}

STEP 4

olve the equation for the number of women who work full-time and have children.
Number of women who work full−time and have children=27×27Number\, of\, women\, who\, work\, full-time\, and\, have\, children = \frac{}{27} \times27

STEP 5

Calculate the number of women who work full-time and have children.
Number of women who work full−time and have children=5Number\, of\, women\, who\, work\, full-time\, and\, have\, children =5

STEP 6

Now that we have the number of women who work full-time and have children, we can find the number of women who work full-time but do not have children. This is given by the total number of women who work full-time minus the number of women who work full-time and have children.
Number of women who work full−time but do not have children=Total number of women who work full−time−Number of women who work full−time and have childrenNumber\, of\, women\, who\, work\, full-time\, but\, do\, not\, have\, children = Total\, number\, of\, women\, who\, work\, full-time - Number\, of\, women\, who\, work\, full-time\, and\, have\, children

STEP 7

Plug in the values for the total number of women who work full-time and the number of women who work full-time and have children to calculate the number of women who work full-time but do not have children.
Number of women who work full−time but do not have children=30−5Number\, of\, women\, who\, work\, full-time\, but\, do\, not\, have\, children =30 -5

STEP 8

Calculate the number of women who work full-time but do not have children.
Number of women who work full−time but do not have children=30−5=25Number\, of\, women\, who\, work\, full-time\, but\, do\, not\, have\, children =30 -5 =25

STEP 9

Similarly, we can find the number of women who do not work full-time but have children. This is given by the total number of women who have children minus the number of women who work full-time and have children.
Number of women who do not work full−time but have children=Total number of women who have children−Number of women who work full−time and have childrenNumber\, of\, women\, who\, do\, not\, work\, full-time\, but\, have\, children = Total\, number\, of\, women\, who\, have\, children - Number\, of\, women\, who\, work\, full-time\, and\, have\, children

STEP 10

Plug in the values for the total number of women who have children and the number of women who work full-time and have children to calculate the number of women who do not work full-time but have children.
Number of women who do not work full−time but have children=27−5Number\, of\, women\, who\, do\, not\, work\, full-time\, but\, have\, children =27 -5

STEP 11

Calculate the number of women who do not work full-time but have children.
Number of women who do not work full−time but have children=27−5=22Number\, of\, women\, who\, do\, not\, work\, full-time\, but\, have\, children =27 -5 =22So, in the Venn diagram, the number of women who work full-time and have children is5, the number of women who work full-time but do not have children is25, and the number of women who do not work full-time but have children is22.

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