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InterviewSolution
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An experiment consists of rolling die until a 2 appears.How many elements of the sample space correspond to the event that 2appears on the kth roll of the die?How many element of the sample space correspond to the event that 2appears not later than the kth roll of the die? |
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Answer» In a through of a die there is 6 sample points. (i) If 2 appears on the kth roll of the die. So, first (k-1) roll have 5 outcomes each and kth roll results 2 i.e., 1 outcome. `therefore" Number of element of sample space correspond to the event that 2 appears on the kth roll of the die" =5^(k-1)` (ii) If we consider that 2 appears later than kth roll of the die. then it is possible that 2 comes in first throw i.e., 1 octcome. If 2 does not appear in first throw, then outcomes will be 5 and 2 comes in second throw i.i., 1 outcome, possible outcome `= 5xx1=5` Similarly, if 2 does not appear in second throw and appears in third throw. `therefore" ""Possible outcomes"=5xx5xx1` `"Given"" ""Series"=1+5+5xx5+5xx5xx5+...+5^(k-1)` `=1+5+5^(2)+5^(3)+...+5^(k-1)` `=(1(5^(k-1)))/(5-1)=(5^(k-1))/(4)` |
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