A fair die is rolled. The probability that the first time 1 occurs at an even throw, is
A
16
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B
511
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C
611
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D
536
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Solution
The correct option is B511 Let E be the event of getting 1 in a die. ⇒P(E)=16andP(¯E)=56 ∴ P(first time 1 occurs at the even throw) =t2ort4ort6ort8 . . . and so on ={P(¯E)P(E)}+{P(¯E)P(¯E)P(¯E)P(E)}+⋯∞=(56)(16)+(56)3(16)+(56)5(16)+⋯∞=5361−2536=511