Question

A local university found it could classify its students into one of three general categories: morning students (49%), afternoon students (27%), and evening students. 36% of the morning students, 26% of the afternoon students, and 16% of the evening students live on campus. What is the probability a non-Morning student does not live on campus? Question 1 Of 45 bank accounts at a small bank, 28 accounts have values of less than $1,000 and the rest have values of at least $1,000. Suppose 4 accounts are randomly sampled. (See exercise 9 on page 184 of your textbook for a similar problem.) Question 2 What is the probability that exactly 3 of the 4 accounts have values of at least $1,000?

Answer 1

Ans: - Given that, A local University found it could classify ete studente into one of there general categorus as below: Morning studente – 497 Afternoon Students – 274 Evening students – 100 (49+27) = 100 – 76 – 241. let M denotes Morning Students, a denotes Afternoon students and E denotes Evening Students then we get, probability of selecting a student P(M)=497.= 0.49 © PCA) z 27.1. -0.27 → @ PCC) = 24.7 70.24 → Also given, 36.1. of Morning students live on campus (c) p(inc) = 36t. of P(x) = 36 x 6.49= 0.1764 Plung) = 0.1784 - 26t of Afternoon students live on Campus (c) planc) = 264. of '0.27 = 2X0.27 = 0.0702 26 100

– 16 f. campusle). Pland) - 0.0702 5. of the Evening studente live on P(End) = 164 of 0.24 - 0.0384 P (Enc) = 0.0384 → © U TA (00 live on students of the Evening - - 26t. of Afternoon students live on campus 100-26 = 744. of Afternoon I does not live on campus. (D) & Pland) = 74% of 0.27 = 14 0.27= 0.1998 e. P(AND) = 0.1998 0 - a 16 y. of the Evening students Campus D 100 -16 = 841 of Evening studer does not live on campus CD) o P(End) - 84.4. of 0.24 € Too PLEND)=0.2016 0 Now consider, Probability of non Morning Student does not live on Campus = 60.24 0.2016

con - probability that an Afternoon student (Axdoce not live on campus (6) probability than an Evening student(Edees not live on Campus (6) (from east 18) - P(AnD) & (End) = 0.1998 + 0.2016 = 0.4014 i probability that a non morning student does not live on Campus = 0.4014 2. Given that, there are 45 bank accounts and among them 28 accounts have values of less than $1000 and the rest (45-28=17) have values of at least $1000. here, - no. of bank accounts having values of atleast $1000 = 17. Now consider, mo. of ways of randomly selecting 4 Bank accounts = n() = Selecting 4 from 45 Bank accounts

= n()= 464 = 451 - 455 148995 40 (45-4)! 4!44! neo. 148995 ->© How consider, no. of ways of selecting exactly 3 of the 4 Bank account have values of at least $1000 = n(A) = ? M(A) = selecting 3 Bank accourite from 17 Bank accounts and one from 28 Bank accounts Ww) Itsz x 24 = 3:(173) wwe ze X 28 = 680 x 28 c19040 17 x 28 (71 In(A)= 19040 0 Now consider from Ears 0 10, probability that exactly s of the 4 have valued atleast $ 1000 = P(A) = accourte & PLA) = 190cpo 20.0278 Tuggas. .: TPCA) = 0.1248] Required Probability, P(A) = 0.12 78.