Question

probability of independent events: decimal answers
at a local college, 76 of the male students are smokers and 124 are non - smokers. of the female students, 38 are smokers and 152 are non - smokers. a male student and a female student from the college are randomly selected for a survey. what is the probability that both are smokers?
do not round your answer. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the probability of selecting a male smoker

The total number of male students is \(76 + 124=200\). The probability of selecting a male smoker \(P(M)=\frac{76}{200}\).

Step2: Calculate the probability of selecting a female smoker

The total number of female students is \(38+152 = 190\). The probability of selecting a female smoker \(P(F)=\frac{38}{190}\).

Step3: Use the formula for independent - events probability

Since the events of selecting a male and a female are independent, the probability that both are smokers is \(P = P(M)\times P(F)\).
Substitute the values: \(P=\frac{76}{200}\times\frac{38}{190}\)

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Answer:

\(0.076\)