Question

Homework: Chapter 3 Review Homework Save Score: 0.33 of 1 pt 13 of 38 (18 complete) HW Score: 31.45%, 11.95 of 38 pts 3.2.17 In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 550 carries a mutation of the BRCA Question Help * 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. The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is 0.80 Round to one decimal place as needed.) (b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer The probability that a randomly selected woman will carry the gene mutation and develop breast cancer is. Round to four decimal places as needed.)

Answer 1

We are given the following probabilities:

P(woman will develop breast cancer) = 1/10

P(woman has mutation of BRCA gene) = 1/550

P(woman will develop breast cancer | woman has mutation of BRCA gene) = 8/10

(a)

Now, we are asked to calculate the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is given by:

P(woman will develop breast cancer | woman has mutation of BRCA gene) = 8/10 = 0.8

(b)

Now, we are asked to calculate the probability of a randomly selected woman carrying a mutation of the BRCA gene and that she will develop breast cancer too. This probability is given by:

$\begin{align*} P(\text{gene mutation } \cap \text{ developing breast cancer} ) &= P(\text{gene mutation}) * P(\text{developing breast cancer } | \text{ gene mutation}) \\ &\text{[Using } P(A\cap B) = P(A)*P(B|A)] \\ &= \frac{1}{550} *\frac{8}{10} \\ &= 0.001454545 \\ &\approx 0.0015 \ \ \ \text{[Rounded to 4 decimal places]} \end{align*}$

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.