I haven't used Bayes' theorem much before so any help would be greatly appreciated.Suppose you are given following data.5% of the population have heart disease.If you have heart disease, the probability that you have high blood pressure is 90%If you do not have heart disease, the probability that you have high blood pressure is 15%What is the probability that a person chosen at random from the population has high blood pressure? P ( B ) = P ( B | H ) P ( H ) + P ( B | H ′ ) P ( H ′ ) P ( B ) = ( .9 ) ( .05 ) + ( .15 ) ( .95 ) = .1875Using Bayes Theorem calculate the probability that the person has heart disease, if they have high blood pressure. P ( H | B ) = P ( B | H ) P ( H ) P ( B ) ( .9 ) ( .05 ) / .1875 = .24Using Bayes Theorem calculate the probability that the person has heart disease, if they do not have high blood pressure. P ( H | B ′ ) = P ( B ′ | H ) P ( B ′ ) P ( H ) When I sub in for this part I'm getting an invalid answer

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I haven&#039;t used Bayes&#039; theorem much before so any help would be greatly appreciated.Suppose you are given following data.5% of the population have heart disease.If you have heart disease, the probability that you have high blood pressure is 90%If you do not have heart disease, the probability that you have high blood pressure is 15%What is the probability that a person chosen at random from the population has high blood pressure?  P  (  B  )  =  P  (  B      |    H  )  P  (  H  )  +  P  (  B      |        H    ′    )  P  (      H    ′    )  P  (  B  )  =  (  .9  )  (  .05  )  +  (  .15  )  (  .95  )  =  .1875Using Bayes Theorem calculate the probability that the person has heart disease, if they have high blood pressure.  P  (  H      |    B  )  =            P      (      B              |            H      )      P      (      H      )              P      (      B      )        (  .9  )  (  .05  )      /    .1875  =  .24Using Bayes Theorem calculate the probability that the person has heart disease, if they do not have high blood pressure.  P  (  H      |        B    ′    )  =            P      (              B        ′                    |            H      )      P      (              B        ′            )              P      (      H      )      When I sub in for this part I&#039;m getting an invalid answer

Biardiask3zd · Accepted Answer

Step 1  P  (  H      |    B  )  =                    P        (        H        ∧        B        )                    P        (        B        )              =                    P        (        B                  |                H        )        P        (        H        )                    P        (        B        )            for the second is fine.Step 2So analogously for the third  P  (  H      |        B    ′    )  =                    P        (        H        ∧                  B          ′                )                    P        (                  B          ′                )              =                    P        (                  B          ′                          |                H        )        P        (        H        )                    P        (                  B          ′                )            and use that   P  (      B    ′    )  =  1  −  P  (  B  ) and   P  (      B    ′        |    H  )  =  1  −  P  (  B      |    H  ). You know all the values already.

Kenna Stanton · Accepted Answer

Explanation:The answer is       3    16    ..You divide and conquer, so the probability that someone has heart disease and high blood pressure is   (      1    20    )  (      9    10    ), which is       9    200  . The probability that someone doesn&#039;t have heart disease and has high blood pressure is   (      1    20    )      3    20  , which is       57    400  .       9    200   is the same as       18    400  . If you add these two fractions, you get       75    400  , or       3    16  .

5% of the population have heart disease. If you have heart disease, the probability that you have high blood pressure is 90% If you do not have heart disease, the probability that you have high blood pressure is 15%

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