Chapter 2: Q. 2.3 (page 48)
Two dice are thrown. Let be the event that the sum of the dice is odd, let be the event that at least one of the dice lands on , and let be the event that the sum is . Describe the eventslocalid="1649252717741" .
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From a group of first-year students,sophomores, juniors, andseniors, a committee of size is randomly selected. Find the probability that the committee will consist of
from each class;
sophomores and juniors;
only sophomores or juniors.
The chess clubs of two schools consist of, respectively, players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that
(a) Rebecca and Elise will be paired?
(b) Rebecca and Elise will be chosen to represent their schools but will not play each other?
(c) either Rebecca or Elise will be chosen to represent her school?
The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a, the player loses; if the sum is either a or an , the player wins. If the outcome is anything else, the player continues to roll the dice until she rolls either the initial outcome or a . If the comes first, the player loses, whereas if the initial outcome reoccurs before the appears, the player wins. Compute the probability of a player winning at craps.
Hint: Let denote the event that the initial outcome is and the player wins. The desired probability is . To compute , define the events to be the event that the initial sum is i and the player wins on the nth roll. Argue that
Consider an experiment whose sample space consists of a countably infinite number of points. Show that not all points can be equally likely. Can all points have a positive probability of occurring?
A total of percent of American males smoke cigarettes, percent smoke cigars, and percent smoke both cigars and cigarettes.
(a)What percentage of males smokes neither cigars nor cigarettes?
(b)What percentage smokes cigars but not cigarettes?
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