A test for the presence of a certain disease has probability 0.2 of giving a false-positive result (indicating that an individua
l has the disease when this is not the case) and probability 0.1 of giving a false-negative result. Suppose that 10 individuals are tested, 5 of whom have the disease and 5 whom do not. Let X be the number of positive readings that result.
a. Explain why X does not have a binomial distribution.
b. Find the probability that exactly 3 of the 10 test results is positive?
a. Explain why X does not have a binomial distribution.
b. Find the probability that exactly 3 of the 10 test results is positive?
1 answer:
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Answer:
The probability that a woman in her 60s has breast cancer given that she gets a positive mammogram is 0.0276.
Step-by-step explanation:
Let a set be events that have occurred be denoted as:
S = {A₁, A₂, A₃,..., Aₙ}
The Bayes' theorem states that the conditional probability of an event, say <em>A</em>ₙ given that another event, say <em>X</em> has already occurred is given by:
The disease Breast cancer is being studied among women of age 60s.
Denote the events as follows:
<em>B</em> = a women in their 60s has breast cancer
+ = the mammograms detects the breast cancer
The information provided is:
Compute the value of P (B|+) using the Bayes' theorem as follows:
Thus, the probability that a woman in her 60s has breast cancer given that she gets a positive mammogram is 0.0276.