Respuesta :
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,
[tex]P(\frac{L}{S})=\frac{P(L\cap S)}{P(S)}[/tex]
[tex]=\frac{0.063}{0.249}[/tex]
[tex]=0.253012048193[/tex]
[tex]=25.3012048193\%[/tex]
[tex]\approx 25.30\%[/tex]
