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Probability

This document presents a probability analysis by a social worker and a school guidance counselor regarding children under 18 years old and employment status of married couples. The first part calculates probabilities concerning randomly selected children (ages 6-10, over 5, and under 1). The second part assesses the likelihood of married couples with both spouses working, having one or more children under 18, and specific employment scenarios (e.g., only the husband working). The calculations utilize basic probability principles to derive actionable insights.

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Probability

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  1. Probability

  2. Question 1 • A Social worker for a child advocacy center has a caseload of 24 children under the age of 18. Her case load by age is as follows: • What is the probability that one of her clients, selected at random is: • Between 6 and 10 years old? • More than 5 years old? • Less than 1 year old?

  3. Solution Open an excel spreadsheet and enter given data.

  4. The probability that a client selected at random is between 6 and 10 years old: • E= the event of selecting a client between 6 and 10 years • P(E)= (number of cases between 6 and 10)/(total number of cases)

  5. The probability that a client selected at random is more than 5 years old: • A= the event of selecting a client more than 5 years old • B= the event of selecting a client between 6 and 10 • C= the event of selecting a client between 11 and 14 • D= the event of selecting a client between 15 and 17 • P(A)= P(B)+P(C)+P(D)

  6. The probability that a client selected at random is less than 1 year old: • E= the event of selecting a client less than 1 year • P(E)= (number of cases under 1)/(total number of cases)

  7. Question 2 • A guidance counselor at a middle school collected the following information regarding the employment status of married couples within his school’s boundaries.

  8. The probability that for married couple selected at random, both spouses work: • E= the event of selecting a married couple with both spouses working • P(E)=(Total of both couples working)/(Overall total)

  9. The probability that for married couple selected at random, the couple has one child under age 18: • E= the event of selecting a married couple with 1 child under age 18 • P(E)=(Total of couples with 1 child)/(Overall total)

  10. The probability that for married couple selected at random, the couple has 2 or more children under age 18 and both spouse work: • E= the event of selecting a married couple with 2 or more children and both spouses working • A= number of couples with 2 or more children and both couples working • B= overall total • P(E)= A/B

  11. The probability that for married couple selected at random, the couple has no children or only the husband works: • Steps: • E= the event of selecting a married couple with no children or only husband works • Find the probability of couple with no children • A= the event of selecting couple with no children • P(A)=(Total of couples with no children)/(Overall total) • Find the find the probability that only husband works • B= the event of selecting a couple with only husband working • P(B)= (Total of couples with only husband working)/(Overall total) • Find the probability that only husband works and no children • C= the event of selecting a couple with only husband working and no children • P(C)= (Total of couples with only husband working and no children)/(Overall total)

  12. The probability that for married couple selected at random, the couple has no children or only the husband works: • Steps: • Find the probability of couple with no children • A= the event of selecting couple with no children • P(A)=(Total of couples with no children)/(Overall total)

  13. The probability that for married couple selected at random, the couple has no children or only the husband works: • Steps: • Find the find the probability that only husband works: • B= the event of selecting a couple with only husband working • P(B)= (Total of couples with only husband working)/(Overall total)

  14. The probability that for married couple selected at random, the couple has no children or only the husband works: • Steps: • Find the probability that only husband works and no children • C= the event of selecting a couple with only husband working and no children • P(C)= (Total of couples with only husband working and no children)/(Overall total)

  15. The probability that for married couple selected at random, the couple has no children or only the husband works: • Steps: • E= the event of selecting a married couple with no children or only husband works • P(E)= P(A)+P(B)-P(C)

  16. CSTEM Web link http://www.cis.famu.edu/~cdellor/math/ • Presentation slides • Problems • Guidelines • Learning materials

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