1.

Two person A and B have 16 and 15 fair coin respectively. If both of them tosses all the coin then probability that A gets more head than B is p then the value of 16p is

Answer»


Solution :Let A and B flips equal number of coins
i.e. 15 coins
`P_(A)` = probability that A OBTAINS more heads than B
`P_(B)` = probability that B obtains more heads than A
`P_(D)` = probability that A obtains as many heads as B
Such that `P_(A) + P_(B) +P_(D) = 1` ...(i)
DUE to symmetry `P_(A) = P_(B)` as both FLIP equal number of coins.
Now 'A' flips extra coin (`16^(TH)` coin).
If it gives tail then does not contribute but if it gives HEAD then A gets more head than B required probability = `P_(A) + 1/2.P_(D)`
`=P_(A) + 1/(2)(1-P_(A)-P_(B)) = 1/2`.


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