# If 3 out of 7 people are smokers and 4 out of 15 people are smokers who will get lung cancer, what is the probability of getting lung caner if you are a smoker?

Mar 16, 2017

color(green)(8/9) or color(green)(88.bar8%)

#### Explanation:

If $A$ is the probability of smoking:
$\textcolor{w h i t e}{\text{XXX")P(A) = 3/7color(white)("XX}}$(given)

If $B$ is the probability of getting lung cancer, then the probability of smoking and getting lung cancer is
$\textcolor{w h i t e}{\text{XXX")P(B & A) = 4/15color(white)("XX}}$(given)

The probability of getting lung cancer ($B$) given smoking ($A$) is
color(white)("XXX")P(B|A) = (P(A&B))/(P(A))
color(white)("XXXXXXXX") =(4/15)/(3/10) =(4 * 10)/(15 * 3) = 40/45=8/9=88.bar8%