Question

research has shown that approximately 1 woman in 600 carries a mutation of a particular gene. about 46% of women with this mutation develop bladder cancer. find the probability that a randomly selected woman will carry the mutation of this gene and will develop bladder cancer.

the probability that a randomly selected woman will carry the gene mutation and develop bladder cancer is
(round to four decimal places as needed.)

Explanation:

Define events and identify given probabilities

Using the Conditional Probability Notation knowledge point

$$
LATEXBLOCK0
$$

Apply multiplication rule for joint probability

Using the Multiplication Rule for Probability knowledge point

$$
LATEXBLOCK1
$$

Calculate and round the final value

We compute the decimal value and round to four decimal places:

$$
LATEXBLOCK2
$$

Answer:

The probability that a randomly selected woman will carry the gene mutation and develop bladder cancer is <blank>0.0008</blank>
(Round to four decimal places as needed.)