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Chapter 2: Q. 2.41 (page 51)
If a die is rolled times, what is the probability that
comes up at least once?
the probability that comes up at least once is.
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Let and be three events. Find expressions for the events so that, of and
only occurs;
both and, but not, occur;
at least one of the events occurs;
at least two of the events occur;
all three events occur;
none of the events occurs;
at most one of the events occurs;
at most two of the events occur;
exactly two of the events occur;
at most three of the events occur.
Use induction to generalize Bonferroni’s inequality to events. That is, show that
.
A basketball team consists of frontcourt and backcourt players. If players are divided into roommates at random, what is the probability that there will be exactly two roommate pairs made up of a backcourt and a frontcourt player?
Prove Boole’s inequality:
An urn contains red, blue, and green balls. If a set of balls is randomly selected, what is the probability that each of the balls will be
(a) of the same color?
(b) of different colors? Repeat under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next selection. This is known as sampling with replacement .
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