Question

According to the American Lung Association 7% of the population has lung disease. Of the people having lung disease 90% are smokers. Of the people not having lung disease 20% are smokers. What are the chances that a smoker has lung disease?

Answer 1

Answer:

The chances that a smoker has lung disease 25.30%.

Step-by-step explanation:

Let L is the event of the lung disease and S is the event of being smoker,

According to the question,

The probability of lung disease, P(L) = 7 % = 0.07,

⇒ The probability of not having lung disease, P(L') = 100 % - 7 % =  93 % = 0.93,

The probability of the people having lung disease who are smokers,

P(L∩S) = 90% of 0.07 = 6.3% = 0.063,

The probability of the people not having lung disease who are smokers,

P(L'∩S) = 20% of 0.93 = 18.60% = 0.186,

Thus, the total probability of being smoker, P(S) = P(L∩S) + P(L'∩S) = 0.063 + 0.186 = 0.249,

Hence, the probability that a smoker has lung disease,

$P(\frac{L}{S})=\frac{P(L\cap S)}{P(S)}$

$=\frac{0.063}{0.249}$

$=0.253012048193$

$=25.3012048193\%$

$\approx 25.30\%$