contestada

In the general population, one woman in eight will develop breast
cancer. Research has shown that 1 woman in 600 carries a mutation of
the BRCA gene. Eight out of 10 women with this mutation develop
breast cancer.
a) Find the probability that a randomly selected woman will develop
breast cancer given that she has a mutation of the BRCA gene. b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop and will develop breast cancer? c) are the events of carrying this mutation and developing Brest cancer independent or dependent?​

Respuesta :

Answer:

a) 8/10

b) [tex]0.001 \overline{33}[/tex]

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 = [tex]0.001 \overline{33}[/tex]

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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