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# Calculate conditional probabilities

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• "29% of men admitted they had cheated" means that total at the bottom of the column labeled 'Male cheating' becomes .29 x 203 = 59
• "compared with 18.5% of women" implies this percent of females had cheated, or the total in the 'Female cheating' column is .185 x 203 = 38

Female cheating Female not cheating Total Male cheating Male not cheating Total
Male right Female right
Male wrong Female wrong
Total 203 Total 203

• "Eighty percent of women's inferences about fidelity or infidelity were correct" means 0.80 x 203 = 162 goes in what cell?
• "men were even better, accurate 94 percent of the time" means .94 x 203 = 191 goes in what cell?

These values will allow for the rest of the 'Total' cells to be filled in but the final sentence of the report provides the two internal cell values representing the intersection of the contingencies: Male right if Female cheating and Female right if Male cheating.
Hence
P(Male right | Female cheating) = .75 and P(Female right | Male cheating) = .41,
which reflects the claim in the title of the report and the first part of the first sentence.

So what exactly did they mean in the first paragraph's claim, "[men] are more likely to suspect infidelities that do not exist,"?

P(Male wrong | Female not cheating) > P(Female wrong | Male not cheating).
OR
P(Female not cheating | Male wrong) > P(Male not cheating | Female wrong)?

That is, are they conditioning on 'not cheating' OR 'being wrong'?

Once you have filled in the tables properly, calculate the conditional probabilities to see which inequality is the correct one.

Show your work and clearly interpret the correct conditional probability that the article is reporting.

https://brainmass.com/statistics/probability/calculate-conditional-probabilities-343125

#### Solution Preview

• "29% of men admitted they had cheated" means that total at the bottom of the column labeled 'Male cheating' becomes .29 x 203 = 59
• "compared with 18.5% of women" implies this percent of females had cheated, or the total in the 'Female cheating' column is .185 x 203 = 38

Female cheating Female not cheating Total Male cheating Male not cheating Total
Male right 0.75 x 38
= 29 191 - 29
= 162 0.94 x 203
= 191 Female right 0.41 x 59
= 24 162 - 24
= 138 0.80 x 203 = 162
Male wrong 38 - 29
= 9 12 - 9
= 3 203 - 191
= 12 Female wrong 59 - 24
= 35 41 - 35
= 6 203 - 162
= 41
Total 0.185 x 203 = 38 203 - 38 ...

#### Solution Summary

The solution calculates conditional probabilities for values of female and males cheating. A complete, neat and step-by-step solution is provided in the attached file.

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