SOLUTION: There are 15 problems on a test, and you have answered 12 of them correctly. To demonstrate the quality of your work, your professor chooses three of the problems at random.
(a)
Algebra ->
Probability-and-statistics
-> SOLUTION: There are 15 problems on a test, and you have answered 12 of them correctly. To demonstrate the quality of your work, your professor chooses three of the problems at random.
(a)
Log On
Question 694834: There are 15 problems on a test, and you have answered 12 of them correctly. To demonstrate the quality of your work, your professor chooses three of the problems at random.
(a) What is the probability that all of the problems chosen are correctly answered?
(b) What is the probability that exactly one of the problems chosen is correctly answered?
(c) What is the expected number of correctly answered problems chosen? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! There are 15 problems on a test, and you have answered 12 of them correctly. To demonstrate the quality of your work, your professor chooses three of the problems at random.
(a) What is the probability that all of the problems chosen are correctly answered?
# of ways to succeed: 12C3
# of possible outcomes: 15C3
---
P(3 correct) = 12C3/15C3 = 0.4835
-----------------------------------------
(b) What is the probability that exactly one of the problems chosen is correctly answered?
# of ways to succeed: (12C1*3C2) = 12*3 = 36
# of possible outcomes: 15C3
P(exactly 1 is correct) = 36/455 = 0.07912
------------------------------------------
(c) What is the expected number of correctly answered problems chosen?
E(x) = 0*P(x=0)+1*P(x=1)+2*P(x=2)
I'll leave that to you.
Cheers,
Stan H.
==================
(