Question

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?

Answer 1

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

Explanation:

If `A` is the probability of smoking:
`color(white)("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
`color(white)("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%`