Suppose that the probability for a student to get a free lift to a university on
ID: 3134299 • Letter: S
Question
Suppose that the probability for a student to get a free lift to a university on any morning is 0.4. The student needs to get a taxi if she/he does not get a lift and she/he needs to pay 20 QAR for a Taxi.. a. Determine the probability that in a week (five days), the student will get a lift only twice? b. Determine the probability that the student will get his/her first lift on the third day? c. Suppose a given month with 20 days. What is expectation of the amount of money that the student needs to pay in a month. (a) What is the mean number of days until eight computers fail in the same day?Explanation / Answer
the probability for a student to get a free lift to a university on any morning=p=0.4
hence the probability of not getting a free lift to a university on any morning=1-0.4=0.6
a) let X denote the number of times a student get a lift in 5 days.
so X~Bin(5,0.4)
hence pmf of X is P[X=x]=5Cx0.4x(1-0.4)5-x
hence the probability that the student will get 2 lifts is
P[X=2]=5C20.420.63=0.3456 [answer]
b) the probability that the student will get his/her first lift on the third day
=probability that the student will not get a lift on the first day*probability that the student will not get a lift on the second day*probability that the student will get a lift on the third day
=0.6*0.6*0.4=0.144 [answer]
c) let Y denotes the amount the student need to pay on one day.
so if he/she gets a free lift he/she need not to pay anything. hence Y=0 with probability 0.4
if he/she does not get a free lift he/she needs to pay 20 QAR for a taxi. so Y=20 with probability 0.6
hence the expected amount of money that the student need to pay on one day is
E[Y]=0*0.4+20*0.6=12 QAR
hence in a month or 20 days the expected amount is 20*E[Y]=20*12=240 QAR [answer]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.