In a certain population of women, 4 percent have had breast cancer, 20% are smokers, and 3% are smokers and have had breast cancer. What is the probability that a woman selected at random has had cancer or smokes, or both? Report with accuracy to 2 decimals (as a proportion, not percentage).

We want to calculate this probability:

And we can use the total probability rule and we have this:

The probability that a woman selected at random has had cancer or smokes, or both is 0.21

Step-by-step explanation:

For this case we define the following events

B= the women selected had breast cancer

S= the women selected is a smoker

= the women selected is a smoker and had breat cancer

And for this case we have the following probabilities given:

And we want to calculate this probability:

And we can use the total probability rule and we have this:

The probability that a woman selected at random has had cancer or smokes, or both is 0.21

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.