Answer:
[tex] P(B)= 0.04 , P(S) = 0.2 , P(B \cap S) =0.03[/tex]
We want to calculate this probability:
[tex] P(B \cup S)[/tex]
And we can use the total probability rule and we have this:
[tex] P(B \cup S) = P(B) +P(S) -P(B \cap S) = 0.04+0.2- 0.03= 0.21[/tex]
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
[tex]B \cap S[/tex]= the women selected is a smoker and had breat cancer
And for this case we have the following probabilities given:
[tex] P(B)= 0.04 , P(S) = 0.2 , P(B \cap S) =0.03[/tex]
And we want to calculate this probability:
[tex] P(B \cup S)[/tex]
And we can use the total probability rule and we have this:
[tex] P(B \cup S) = P(B) +P(S) -P(B \cap S) = 0.04+0.2- 0.03= 0.21[/tex]
The probability that a woman selected at random has had cancer or smokes, or both is 0.21
