The probability of receiving a "false positive" from a mammogram is 7%. What is the probability that out of 10 mammograms, a patient receives at least 1 false positive?
Pr(at least one false)=1-pr(gettingnofalse)=1-.83^10
.83^10=.155, so pr(getting at least one false in 10) is 1-.155=.845
Hmmm. So, the thought of annual mammograms is comforting?
Since the false positive p = .07, wouldn't you need 1-.93 as P of not getting false positive?
Yes you definitely do need 1-0.93. Psydag, you are correct!
To find the probability that a patient receives at least 1 false positive out of 10 mammograms, we can use the concept of complementary probability.
The complementary probability of an event A is equal to 1 minus the probability of event A occurring. In this case, event A is the patient receiving no false positives out of 10 mammograms.
The probability of receiving a false positive in a single mammogram is 7%, or 0.07 in decimal form. Therefore, the probability of not receiving a false positive in a single mammogram is 1 - 0.07 = 0.93.
Now, we can calculate the probability of the patient receiving no false positives out of 10 mammograms. Since each mammogram is independent of the others, we can use the multiplication rule for independent events.
The probability of not receiving a false positive in all 10 mammograms is (0.93)^10, which is approximately 0.4783.
Finally, to find the probability that the patient receives at least 1 false positive, we subtract the probability of receiving no false positives from 1:
1 - 0.4783 = 0.5217
Therefore, the probability that a patient receives at least 1 false positive out of 10 mammograms is approximately 0.5217 or 52.17%.