Alice thinks of an integer between 0 and 9, and Tom\'s task is to guess this num

Question

Alice thinks of an integer between 0 and 9, and Tom's task is to guess this number. His strategy is as follows: He randomly (i.e., uniformly likely over all possibilities) guesses a number; if this is wrong, he randomly guesses a new number but avoids choosing the number he just guessed, and independent of any other event. In other words, he randomly guesses, but has short term memory of exactly one previous guess. He stops when he guesses correctly. Determine the pmf of the random variable corresponding to the Number of Guesses made by Tom.

Explanation / Answer

given that,

alice thinks of an integer between 0 and 9.

toms task to guess the number.

hes follow strategys?

he guesses randomly and independent of other events,

let x be the number of guesses,

also x be the number of failures before get success,

.... we have series of independent trails, in each trail the probability of success is same..

then the probability that there are x guesses preceedings the first success (IF GUESS IS CORRECT)

is given by q^x(p)

p(x)={ q^x(p) :x=0,1,2,3,4,......

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