On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. The test predicted that Erin will not have a heart attack. What is the probability after the test was taken that she will have a heart attack?

A. 0.4051

B. 0.5010

C. 0.4653

D. 0.6632

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctorstold her that the reliability of the stress test is 67%. The test predicted that Erin will not have a heart attack. The probability after the test was taken that she will have a heart attack is "B. 0.501."

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InesWalston InesWalston · Answer 2 · 2018-11-30T06:04:20+01:00

Answer:

The probability that she will not have a heart attack and the test predicts that she will is 0.4653 or 46.53%

Step-by-step explanation:

Hint- This a conditional probability problem where Bayes theorem should be applied.

Applying Bayes theorem,

[tex]P(\text{No heart attack}\ |\ \text{Correctly tested})=[/tex]

[tex]\dfrac{P(\text{Correctly tested}\ |\ \text{No heart attack})\cdot P(\text{No heart attack})}{P(\text{Correctly tested})}[/tex]

[tex]P(\text{Correctly\ tested}\ |\ \text{No\ heart\ attack})=67\%=0.67[/tex]

[tex]P(\text{No\ heart\ attack})=1-P(\text{heart\ attack})=1-0.7=0.3[/tex]

[tex]P(\text{Correctly\ tested})=[P(\text{No\ heart\ attack})\times P(\text{Correctly\ tested})]+[P(\text{Heart\ attack})\times (\text{Incorrectly\ tested})][/tex]

[tex]=[0.3\times 0.67]+[0.7\times 0.33]=0.432[/tex]

Putting the values,

[tex]P(\text{No\ heart\ attack}\ |\ \text{Correctly\ tested})=\dfrac{0.67\times 0.3}{0.432} =0.4653[/tex]

∴ There is a probability of 0.4653 or 46.53% chance that she will not have a heart attack even though the test predicts that she will.