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By Nicholas J Giordano; Hisao Nakanishi

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2) 202. Give suitable sample spaces for the following random trials: (a) Throw a die and count the tosses until one ofthe six outcomes has appeared twice. (b) Throw a die and count the tosses until one of the six outcomes has appeared twice in succession. 2) 203. At a sawmill boards are cut into 3-feet lengths, and the remaining pieces smaller than 3 feet are thrown on a heap. Give a suitable sample space for the trial: Choose one of the small parts and note its length (unit: feet). 2) Exercises 37 204.

By o(h) we mean a quantity that goes to zero when h .....

The events Hi are mutually exclusive. The event Hi occurs if there are i - I "failures" and then one "success". Hence we get (see Example 17) 1 (65)i-1 6' P(H i ) = The probability we want is given by P = P(H 1 U H3 Hs u ... ) U = ~[ 1 + GY + GY + ... ] 6 =6'1- (W =0 Hence the probability that B loses his life is 1 - 6/11 = 5/11; that is, the second player has a somewhat greater chance of surviving, as might be expected. The problem can also be solved in another surprisingly simple way. Let T be the event that "A is killed on the first trial".

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