Question

Suppose that a certain college class contains 47 students of these, 28 are sophomores, 27 are business majors, and 8 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a sophomore and a business major? (b) Given that the student selected is a business major, what is the probability that he is also a sophomore? Write your responses as fractions. (If necessary, consult a list of formulas.)

Answer 1

let Let & be the total number of students. . * = 47 A denote the set of 8 students that are Sophomores B denote the set of students that are business majors . . n(A) = 28 NLB) = 27 Given that 8 are neithes sophomores annar bussiness majors . nià MB) = 8 ronà HB) T= Ā UB) X - NLAUB =8 = x-nous? X-8= n(AUB) or fees nAUB) =X-8 = 47-8 = 39 As n(AUB) = n( 994 me 8) - DIAMB) .. nianB) = n(A) thiB) - M CHUB) = 88 +27-39 - 16 ).

- The a - - probability that the student its both sophomore and a bussines major PLANB) PLANB) = n(AMB) 5 16 = 0.2404 0.34 47 (6) Probabity (that a student is sophomore given that the student is a bussiness major) = P(A/B) - PC PP0) PIB) n(ANB) n (B) = = 00592 50.59 n(ARB) = n(B) 16 97
We will calculate the required probabilities by using addition rule of probability.