at a local college, 390 of the male students are smokers and 610 are non-smokers. of the female students, 99 are smokers and 891 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.)

Question

at a local college, 390 of the male students are smokers and 610 are non-smokers. of the female students, 99 are smokers and 891 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.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Probability of Events" ], "new_concepts": [ "Independent Events Probability" ], "current_concepts": [ "Probability of Events", "Independent Events Probability" ] } ## Calculate individual probabilities Using the *Probability of Events* knowledge point $$ \begin{aligned} &\text{Total male students} = 390 + 610 = 1000\ &P(\text{male is a smoker}) = \frac{390}{1000} = 0.39\ &\text{Total female students} = 99 + 891 = 990\ &P(\text{female is a smoker}) = \frac{99}{990} = 0.1 \end{aligned} $$ ## Calculate joint probability Using the *Probability of Events* knowledge point $$ \begin{aligned} &P(\text{both are smokers}) = P(\text{male is a smoker}) \times P(\text{female is a smoker})\ &P(\text{both are smokers}) = 0.39 \times 0.1 = 0.039 \end{aligned} $$ At a local college, 390 of the male students are smokers and 610 are non-smokers. Of the female students, 99 are smokers and 891 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. The probability that both are smokers is 0.039. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Events" ] }

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Question

Explanation:

Calculate individual probabilities

Calculate joint probability

Answer: