STAT 230
FINAL EXAM
WINTER 2001
1. A group of 60 Waterloo students consists of 10 Stats, 30 CS, and 20 AM students.
(a) How many distinct ways can these students be ordered in a row if we do not distinguish
between students in the same degree program?
(b) If the students are ordered at random, find the probability that the Statistics students are
split with 5 at each end of the row.
(c) If 5 students are selected at random (without replacement) give an exact expression for the
probability that 3 are CS students.
(d) Give an appropriate approximation to the probability in (c) and evaluate it numerically.
2. A die is loaded to give the following probabilities
number
1
2
3
4
5
6
probability
.3
.1
.15
.15
.15
.15
The die is rolled (independently) 4 times. Find the probability that
(a) 2 does not occur
(b) neither 2 nor 5 occurs
(c) both 2 and 5 occur
(d) 2 occurs but 5 does not
3.
Five identical bowls are labelled 1,2,3,4, and 5.
Bowl
i
contains
i
white and 5

i
black
balls,
i
= 1
,
2
, . . . ,
5.
A bowl is randomly selected and two balls are randomly chosen (without
replacement) from the contents of the bowl.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '06
 various
 Probability, Probability theory, probability density function, SafeWeek.

Click to edit the document details