\"After taking 10 mammograms, a patient has a 50% chance of having had at least

Question

"After taking 10 mammograms, a patient has a 50% chance of having had at least one false alarm." (A false alarm is a false-positive result.) Given this information (from Elmore et al. 2005), and assuming that false alarms are independent of each other, what is the probability of a false alarm on a single mammogram? How would you solve this problem without using the log? We were told to define the events like this and solve. A=be the event that there is at least one false alarm among 10 mammograms F=be the event that there is a false alarm in a single mammogram P(A)=0.5 Find P(F)=p Our teacher said to use the complement of A to help us find the probability. Any help would be great!

Explanation / Answer

P(F) = p

P(A) = P(at least one false alarm) = 1 - P(no false alarm) = 1 - (1 -p)10

0.5 = 1 - (1 -p)10

or, (1 -p)10 = 0.5

or, 1 - p = 0.933

or, p = 0.067 (ans)

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