PLEAS HELP! I have an exam coming up and still cannot figure out how to do these

Question

PLEAS HELP! I have an exam coming up and still cannot figure out how to do these basic probability problems :[ Can someone explain how to do these along with the answer? Thanks in advance! Here is the relevant information:

You are hanging out with your BIOL321 Genetics study group talking about personalized medicine and the use of genetic tests to predict diseases like cancer. A member of your study group pulls up some statistics from a study with breast cancer: 12% of women in the US will develop breast cancer during their lives, 0.2% of women have mutations in the BRCA2 gene that are associated with breast cancer, and 1.2% of women with breast cancer have those mutations in the BRCA2 gene. Members of your group discuss that the odds of getting break cancer are pretty high at 12% but then note that very few women with breast cancer have these mutations in BRCA2, so it seems like it wouldn’t be very valuable to test for those mutations.

(a) Do you agree with your group? What is your guess as to how informative it might be to know if someone has one of these BRCA2 mutations?

(b) You mention to your group that you know some probability theory and that a specific equation would be useful for calculating the probability of getting breast cancer for carriers of these BRCA2 mutations. What equation would you mention? homework assignment 3: basic probability 3

(c) Calculate the conditional probability of getting breast cancer for a BRCA2 mutation carrier using that equation.

(d) Did knowing the probability theory give you insight beyond your intuition?

Explanation / Answer

Let A be the event that women in the US will develop breast cancer during their lives; B be the event that women with breast cancer have those mutations in the BRCA2 gene. Then A^B (A intersection B) is women have mutations in the BRCA2 gene that are associated with breast cancer.

So, P(A) = 12/100, P(B) = 1.2/100 and P(A ^ B) = 0.2 / 100.

So, P( A U B) = 12/100 + 1.2/100 - 0.2/100 = (12 + 1.2 -0.2 )/100 = 0.13

Yes, I agree with the guess of the group

(b) In order to calculate the probabilty, we need to use the equations of total probabilty and conditional probability as given below:

P(AUB) = P(A) + P(B) - P(A^B0

and P(A/B) = P(A^B)/P(B)

(c) P(A/B) = P(A^B)/P(B) = 0.2/1.2 = 0.167

(d) Yes, definitely.

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