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Chapter 2: Q.47 (page 51)
If there are strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?
The required probability is
.
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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?
If it is assumed that all poker hands are equally likely, what is the probability of being dealt
a flush? (A hand is said to be a flush if all cards are of the same suit.)
one pair? (This occurs when the cards have denominations where andare all distinct.)
two pairs? (This occurs when the cards have denominations where and are all distinct.)
three of a kind? (This occurs when the cards have denominations where and are all distinct.)
four of a kind? (This occurs when the cards have denominations)
Consider Example, which is concerned with the number of runs of wins obtained whenwins and losses are randomly permuted. Now consider the total number of runs鈥攖hat is, win runs plus loss runs鈥攁nd show that
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
A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding if they do and if they do not) and according to their condition, which is rated as good (g), fair (f), or serious (s). Consider an experiment that consists of
the coding of such a patient.
(a) Give the sample space of this experiment.
(b) Let be the event that the patient is in serious condition. Specify the outcomes in .
(c) Let be the event that the patient is uninsured. Specify the outcomes in .
(d) Give all the outcomes in the event .
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