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#### steps_8186

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Assuming that mammography has a sensitivity of 90% and a specificity of 98% and that consecutive tests are independent, what is the probability that a woman with breast cancer will have a negative yearly screening mammogram for
two consecutive years?
a. 1/10
b. 2/10
c. 4/10
d. 1/100
e. 4/100

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D.........

#### numbndumb

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D

They are asking about the probability of FALSE NEGATIVE results of mammogram for 2 consecutive events. FALSE NEGATIVE RATE = 1-seNsitivity = 1-0.9 = 0.1

Now the probability of having 2 false negative results in 2 consecutive yrs are independent events so u multiply the probabilities 0.1*0.1 or 1/10*1/10 =1/100 (option d)

#### steps_8186

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#### devareddy

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Guys, I donot understand why do we have to multiply 1/10 of the first year with the 1/10 of next year as those two tests are independent. Why the answer is not just 1/10. Please explain?

If sensitivity is 90% means, out of 100 diseased 90 were correctly identified as diseased (True Positives) and 10% were missed (False negatives) &

If the specificity is 98% means, out of 100 healthy people 98 were correctly identified as normal (True negatives) and 2 were missed (False positives)

False Negative rate = False negatives/ No. of diseased = 10/100 = 1/10. I can get this far. But the multiplying thing. Elaborate please..........

#### futsalplayer

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Guys, I donot understand why do we have to multiply 1/10 of the first year with the 1/10 of next year as those two tests are independent. Why the answer is not just 1/10. Please explain?

If sensitivity is 90% means, out of 100 diseased 90 were correctly identified as diseased (True Positives) and 10% were missed (False negatives) &

If the specificity is 98% means, out of 100 healthy people 98 were correctly identified as normal (True negatives) and 2 were missed (False positives)

False Negative rate = False negatives/ No. of diseased = 10/100 = 1/10. I can get this far. But the multiplying thing. Elaborate please..........
You have to multiply because we have to find the <probability that a woman with breast cancer will have a negative yearly screening mammogram for two consecutive year>. So she has to have 2 negative yearly screening mammograms for 2 consecutive years.
This type of probability is called COMPOUND PROBABILITY and it can be calculated by multiplying the porbabilities of each independent event.

So we have two independets events with a probability of 1/10 each one; we multiply 1/10*1/10 and we find 1/100 (answer D).

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