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?

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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?

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Answer 1 · 2017-03-16T13:34:06

$\frac{8}{9} or 88 . ¯ 8 %$ $color(green)(8/9) or color(green)(88.bar8%)$

Explanation:

If $A$ $A$ is the probability of smoking:
$XXX P (A) = \frac{3}{7} XX$ $color(white)("XXX")P(A) = 3/7color(white)("XX")$ (given)

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

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

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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?

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