Here is a table of the education level and the sex for our sample: counts Female (F) Male (M) Total High School (HS) 124 117 241 Less than High School (LHS) 136 105 241 More than High School (MHS) 215 177 392 Total 475 400 875 Calculate the probability P(HS and F). Represent your answer as a fraction. Calculate the probability P(F | MHS). Represent your answer as a fraction. Calculate the probability P(F or LHS). Represent your answer as a fraction. Between which group, Male or Female, is the likelihood of having a high school education the highest? Explain, using the appropriate fractions and notation.
Question
Here is a table of the education level and the sex for our sample:
counts Female (F) Male (M) Total High School (HS) 124 117 241 Less than High School (LHS) 136 105 241 More than High School (MHS) 215 177 392 Total 475 400 875 Calculate the probability P(HS and F). Represent your answer as a fraction. Calculate the probability P(F | MHS). Represent your answer as a fraction. Calculate the probability P(F or LHS). Represent your answer as a fraction. Between which group, Male or Female, is the likelihood of having a high school education the highest? Explain, using the appropriate fractions and notation.
Solution
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The probability P(HS and F) is calculated by dividing the number of females with a high school education by the total sample size. From the table, we can see that there are 124 females with a high school education and the total sample size is 875. Therefore, P(HS and F) = 124/875.
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The probability P(F | MHS) is calculated by dividing the number of females with more than a high school education by the total number of individuals with more than a high school education. From the table, we can see that there are 215 females with more than a high school education and the total number of individuals with more than a high school education is 392. Therefore, P(F | MHS) = 215/392.
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The probability P(F or LHS) is calculated by adding the probability of being female and the probability of having less than a high school education. From the table, we can see that there are 475 females and 241 individuals with less than a high school education. Therefore, P(F or LHS) = (475 + 241)/875. However, we are double counting females with less than a high school education, so we need to subtract this group once. There are 136 females with less than a high school education, so P(F or LHS) = (475 + 241 - 136)/875.
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To determine between which group, Male or Female, the likelihood of having a high school education is the highest, we need to calculate the conditional probabilities P(HS | F) and P(HS | M). P(HS | F) = 124/475 and P(HS | M) = 117/400. Comparing these two fractions, we can see that P(HS | F) > P(HS | M), so the likelihood of having a high school education is higher among females.
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