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Chapter 2: Q11SE (page 91)
Suppose that there is a probability of\(\frac{1}{{50}}\)that you will win a certain game. If you play the game 50 times, independently, what is the probability that you will win at least once?
Probability that someone will win at least once is \(1 - {\left( {\frac{{49}}{{50}}} \right)^{50}}\).
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Three studentsA,B, andC,are enrolled in the same class. Suppose thatAattends class 30 percent of the time,Battends class 50 percent of the time, andCattends class 80 percent of the time. If these students attend classindependently of each other, what is (a) the probability that at least one of them will be in class on a particular day and (b) the probability that exactly one of them will be in class on a particular day?
Consider again the conditions of Example 2.3.5, in which the phenotype of an individual was observed and found to be the dominant trait. For which values ofi,(i=1, . . . ,6) is the posterior probability that the parents have the genotypes of event\({{\bf{B}}_{\bf{i}}}\)smaller than the prior probability that the parents have the genotypes of event\({{\bf{B}}_{\bf{i}}}\)?
Suppose that three red balls and three white balls are thrown at random into three boxes and and that all throws are independent. What is the probability that each box contains one red ball and one white ball?
Each time a shopper purchases a tube of toothpaste, he chooses either brand A or brand B. Suppose that for each purchase after the first, the probability is 1/3 that he will choose the same brand that he chose on his preceding purchase and the probability is 2/3 that he will switch brands. If he is equally likely to choose either brand A or brand B on his first purchase, what is the probability that both his first and second purchases will be brand A and both his third and fourth purchases will be brand B?
Suppose that A and B are independent events such that\({\bf{Pr}}\left( {\bf{A}} \right){\bf{ = }}{\raise0.7ex\hbox{\({\bf{1}}\)} \!\mathord{\left/ {\vphantom {{\bf{1}} {\bf{3}}}}\right.}\!\lower0.7ex\hbox{\({\bf{3}}\)}}\)and\({\bf{Pr}}\left( {\bf{B}} \right){\bf{ > 0}}\). What is the value of\({\bf{Pr}}\left( {{\bf{A}} \cup {{\bf{B}}{\bf{c}}}{\bf{|B}}} \right)\)?
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