Survey Respondents Flip CoinsDate: 08/04/97 at 07:21:17 From: Anonymous Subject: Probability I have an advanced math class and I'm stuck on a problem, which is: Respondents are asked to flip a coin in private and answer question A if the result is a head and question B if the result is a tail. Knowing the probability of getting a head or a tail and the probability that question B will be answered "Yes" (it's 0.5), the researcher can then use the total fraction of "Yes" responses to calculate the probability that question A will be answered "Yes." If this survey is administered to 1000 people and 700 people answer "Yes", find the probability that a person will answer "Yes" to question A. Date: 08/04/97 at 16:09:29 From: Doctor Anthony Subject: Re: Probability These problems are best done by laying out the probabilities in tabular form: | A(1/2) B(1/2) | -------------------------------------- YES | .45 .25 | .7 | | | | NO | .05 .25 | .3 ---------------------------------------- | .50 .50 | 1 This table is completed by filling in .25 (= 1/2 x 1/2) in the B/YES box, then .7 as the total for the YES row, so this means A/YES must be .45 B/NO must also be 1/2 x 1/2 = .25 so the B column is .5 The overall total is 1, so A column is also .5 This means that A/NO must be .05 We have been able to complete the table by noting the sums of rows or columns and one or two interior probabilities. The .45 in the A/YES box is the product of the probabilities: Probability of getting question A x probability of answering this YES (1/2) x (prob. of answering YES) = 0.45 Prob. of answering YES to question A = 0.90 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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