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Expected number of tosses under a stopping rule

This type of question, asked 2 times: 12 Apr 2023, 13 Apr 2023. All 2 questions below, oldest first.

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  1. Question 1

    12 Apr 2023

    81
    A fair n(n>1)n(n > 1) faces die is rolled repeatedly until a number less than nn appears. If the mean of the number of tosses required is n9\frac{n}{9}, then nn is equal to

  2. Question 2

    13 Apr 2023

    66
    A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If XX denotes the number of tosses of the coin, then the mean of XX is

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