David Mashley teaches two undergraduate statistics courses at Kansas College. Th
ID: 3125681 • Letter: D
Question
David Mashley teaches two undergraduate statistics courses at Kansas College. The class for Statistics 201 consists of 7 sophomores and 3 juniors. The more advanced course. Statistics 301. has 2 sophomores and 8 juniors enrolled. As an example of a business sampling technique. Professor Mashley randomly selects, from the stack of Statistics 201 registration cards, the class card of one student and then places that card back in the stack. If that student was a sophomore. Mashley draws another card from the Statistics 201 stack; if not, he randomly draws a card from the Statistics 301 group. Are these two draws independent events? What is the probability of a junior's name on the first draw? a junior s name on the second draw, given that a sophomore' name was drawn first? a junior s name on the second draw, given that a junior's name was drawn first? a sophomore's name on both draws? a junior's name on both draws? one sophomore s name and one junior's name on the two draws, regardless of order drawn?Explanation / Answer
statistics 201 consists of 7 sophomores and 3 juniors.
statistics 301 consists of 2 sophomores and 8 juniors.
the professor randomly selects one card from statistics 201 and places it back in the stack.
if the selected student is sophomore then he again selects a card from statistics 201 otherwise from statistics 301.
these two draws are not independent since the second draw depends upon the result of the first draw. the result of the first draw decides from which stack the second draw should be done. so they are not independent.
a) the probability that a junior's name on the first draw is the probability of selecting one junior from 3 juniors out of 10 students of statistics 201.
hence the probability is 3/10 [answer]
b) the probability that a junior's name on the second draw given that a sophomore's name was drawn in the first draw means selecting one from 8 juniors out of 10 students of statistics 301 [as when a sophomore's name was drawn in the first draw then the professor made the second drawing from statistics 301 stack]
hence the probability is 8/10 [answer]
c) the probability that a junior's name on the second draw given that a junior's name was drawn in the first draw means selecting one from 3 juniors out of 10 students of statistics 201 [as when a junior's name was drawn in the first draw then the professor made the second drawing from statistics 201 stack]
hence the probability is 3/10 [answer]
d) the probability that a sophomore's name on both draws is selecting a sophomore from 7 sophomores out of 10 students of statistics 201 in the first draw and selecting a sophomore from 2 sophomores out of 10 students of statistics 301 in the second draw as in the first draw a sophomore is selected
hence the probability=7/10*2/10=14/100=7/50 [answer]
e) the probability that a junior's name on both draws is selecting a junior from 3 sophomores out of 10 students of statistics 201 in the first draw and selecting a junior from 3 juniors out of 10 students of statistics 201 in the second draw as in the first draw a junior is selected
hence the probability=3/10*3/10=9/100 [answer]
f) the probability that one sophomore's name and one junior's name on the two draws,regardless of orde drawn is
[selecting a sophomore from 7 sophomores out of 10 students of statistics 201 in the first draw and selecting a junior from 8 juniors out of 10 students of statistics 301 in the second draw as in the first draw a sophomore is selected] or [selecting a junior from 3 juniors out of 10 students of statistics 201 in the first draw and selecting a sophomore from 7 juniors out of 10 students of statistics 201 in the second draw as in the first draw a junior is selected]
hence the probability=7/10*8/10+3/10*7/10=56/100+21/100=77/100 [answer]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.