5-55. In a random sample of 10,000 college students, a research company found that 35.7% were involved in a
club and 27.8% studied 4 or more hours per day. When they reported their findings, the research company
indicated that 53.4% of college students were either involved in a club or they studied 4 or more hours per day.
Given this information, what is the probability that a college student is involved in a club and studies 4 or more
hours per day?

Respuesta :

The probability that a college student is involved in a club and studies 4 or more  hours per day is 9.92%.

Data and Calculations:

College student population = 10,000

Students involved in a club = 35.7% or 3,570 (10,000 x 35.7%)

Students who studied 4 or more hours per day = 27.8% or 2,780 (10,000 x 27.8%)

Students who involved in a club or studied 4 or more hours per day = 53.4% or 5,340 (10,000 x 53.4%)

The probability that a student, who is involved in a club, studies 4 or more hours per day is 9.92% (35.7% x 27.8%).

Thus, the probability that a student involves in a club and studies 4 or more hours per day is 9.92% or 992 students out of 10,000.

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