Chapter 2: Q8E (page 75)
If three balanced dice are rolled, what is the probability that all three numbers will be the same?
If three balanced dice are rolled, the probability that all three numbers will be the same is \(\frac{1}{{36}}\) .
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Suppose that a balanced die is rolled three times, and let\({X_i}\)denote the number that appears on the ith roll (i = 1, 2, 3). Evaluate\({\rm P}\left( {{X_1} > {X_2} > X3} \right)\).
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?
Suppose that a box contains five coins and that for each coin there is a different probability that a head will be obtained when the coin is tossed. Let \({{\bf{p}}_{\bf{i}}}\)denote the probability of a head when theith coin is tossed \({\bf{i = }}\left( {{\bf{1, \ldots ,5}}} \right)\) and suppose that \({{\bf{p}}_{\bf{1}}}{\bf{ = 0}}\),\({{\bf{p}}_{\bf{2}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{4}}}\) ,\({{\bf{p}}_{\bf{3}}}{\bf{ = }}\frac{{\bf{1}}}{{\bf{2}}}\) ,\({{\bf{p}}_{\bf{4}}}{\bf{ = }}\frac{{\bf{3}}}{{\bf{4}}}\) , and \({{\bf{p}}_{\bf{5}}}{\bf{ = 1}}\).
Consider the World Series of baseball, as described in Exercise 16 of Sec. 2.2. If there is probability p that team A will win any particular game, what is the probability that it will be necessary to play seven games in order to determine the winner of the Series?
Suppose a person rolls two balanced dice twice in succession. Determine the probability that the sum of the two numbers that appear on each of the three rolls will be 7.
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