At a local college,153 of the male students are smokers and 357 are non-smokers. Of the female students,145 are smokers and are 355 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.
To calculate the probability that both a male and a female student are smokers, we need to find the probability of selecting a male smoker and a female smoker, and then multiply them together.
First, let's find the probability of selecting a male smoker. We know that there are 153 male smokers out of a total of 153 + 357 = 510 male students. Therefore, the probability of selecting a male smoker is 153/510.
Next, let's find the probability of selecting a female smoker. We know that there are 145 female smokers out of a total of 145 + 355 = 500 female students. Therefore, the probability of selecting a female smoker is 145/500.
Now, to find the probability that both are smokers, we multiply the two probabilities together:
P(selecting a male smoker and a female smoker) = P(male smoker) * P(female smoker)
= (153/510) * (145/500)
Calculating this gives us the probability that both a male and a female student are smokers.
To find the probability that both the male and female students are smokers, we will use the principle of multiplication.
The probability of selecting a male smoker is 153/510 (number of male smokers divided by the total number of male students).
The probability of selecting a female smoker is 145/500 (number of female smokers divided by the total number of female students).
To find the probability that both are smokers, we multiply the probabilities together:
P(both are smokers) = (153/510) * (145/500)
P(both are smokers) = 0.3 * 0.29
P(both are smokers) = 0.087, or 8.7%
These picks are independent. Picking a male student does not affect the following pick of a female student. Therefore the answer is simply the product of the two probabilities.
153 + 357 = 510 males
male probability = 153/510 = .3
145 + 355 = 500 females
female probability = 145/500 = .29
probability of both happening =.3*.29 = 0.087