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Chapter 2: Problem 41
If a die is rolled 4 times, what is the probability that 6 comes up at least once?
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The chess clubs of two schools consist of, respectively, 8 and 9 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 cach other? (c) either Rebecca or Elise will be chosen to represent her school?
How many people have to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least \(\frac{1}{2} ?\) Assume that all possible monthly outcomes are equally likely.
Poker dice is played by simultaneously rolling 5 dice. Show that (a) \(P\\{\text { no two alike }\\}=.0926\) (b) \(P\\{\text { one pair }\\}=.4630\) (c) \(P\\{\text { two pair }\\}=.2315\) (d) \(P\\{\text { three alike }\\}=.1543\) (e) \(P\\{\text { full house }\\}=.0386\) (f) \(P\\{\text { four alike }\\}=.0193\) (g) \(P\\{\text { five alike }\\}=.0008\)
A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making?
A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding 1 if they do and 0 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 \(A\) be the event that the patient is in serious condition. Specify the outcomes in \(A\) (c) Let \(B\) be the event that the patient is uninsured. Specify the outcomes in \(B\). (d) Give all the outcomes in the event \(B^{c} \cup A\).
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