In the general population, one woman in eight will develop breast
1 answer:
Answer:
a) 8/10
b)
c) Independent events
Step-by-step explanation:
The given information are;
The proportion of women than carries a mutation of the BRCA gene, P(A) = 1/600
The proportion of women in which the mutation develops breast cancer, P(B) = 8/10
a) The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is given as follows;
1 × P(B) = 1 × 8/10 = 8/10
b) The probability, P that a randomly selected woman woman will carry the mutation of the BRCA gene and will develop breast cancer is given as follows;
P(A) × P(B) = 1/600×8/10 = 1/750 =
c) The events are dependent
Given that P(A) × P(B) = P(A∩B), the events of carrying the mutation and developing Breast cancer are independent events.
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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.