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Chapter 2: Q. 2.1 (page 52)
Prove the following relations:
Use the definition of a subset and logical operations.
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Poker dice is played by simultaneously rolling dice. Show that
(a) P{no two alike}
(b) P{one pair}
(c) P{two pair}
(d) P{three alike}
(e) P{full house}
(f) P{four alike}
(g) P{five alike}
A -personal basketball team consists of a guard, a forward, and a center.
If a person is chosen at random from each of three different such teams, what is the probability of selecting a complete team?
What is the probability that all players selected play the same position?
Use induction to generalize Bonferroni鈥檚 inequality to events. That is, show that
.
A group of individuals containing boys and girls is lined up in random order; that is, each of thepermutations is assumed to be equally likely. What is the probability that the person in the ith position, role="math" localid="1648906629368" is a girl?
A box contains marbles: red, green, and blue. Consider an experiment that consists of taking marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.
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