Assume that the class consists of 45 percent freshmen, 20 percent sophomores, 15

Question

Assume that the class consists of 45 percent freshmen, 20 percent sophomores, 15 percent juniors, and 20 percent seniors. Assume further that 50 percent of the freshmen, 50 percent of the sophomores, 25 percent of the juniors, and 20 percent of the seniors plan to go to medical school. One student is selected at random from the class.

(1) What is the probability that the student plans to go to medical school?

(2) If the student plans to go to medical school, what is the probability that he is a sophomore?

Explanation / Answer

Dear Student Thank you for using Chegg!! Let the number of students in class be 100n As per question Type of students Total Students planning forMedical School Number of freshmen = 45n 0.5*45n =22.5n Number of sophomores = 20n 0.5*20n =10n Number of Juniors = 15n 0.25*15n =3.75n Number of seniors = 20n 0.20*20n =4n Total = 100n =40.25n a) Probability That the student plans to go to medical school = Number of students planning for medical school / total number of students = 40.25n / 100n = 0.4025 Solution b) If the student plans to go to medical school, what is the probability that he is a sophomore? = Number of sophomores planning for medical school/ Total number of sophomores = 10n / 20n = 0.5 Solution

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