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In a certain survey, 30% of those questioned are given an incentive to complete the survey. Of those who receive incentives, 80% completed the survey. Of those who do not receive incentives, 25% completed the survey.
a. Find the probability of getting incentives for those who completed the survey. Hint: Use Bayes’ Theorem
b. If one questioned subject is selected at random, find the probability that is completed. Hint: The answer is in part a.

I found the part A answer to be 0.578 by using bayes.
(0.8*0.3)/(0.8*0.3 + 0.25*0.7)

but i have no idea on how to find b. I thought it woudl be .8*.25 because .8 completed the survey with incentives and .25 completed survey so the proabiblity would be 1/(.8*.25).

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  1. a. agree
    b The first term in the denominator is those who got the incentive and completed the survey.
    The second term in the denominator is those who completed the survey without the incentive.
    The sum is all those who completed the survey, which is what you are looking for.

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    Damon

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