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CGP EDU Academic Team
Published on: August 14, 2026
A biased coin that has a probability of getting heads as p (0 < p < 1) is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is 
, then 9p is equal to
Text Solution
Verified by ExpertsThe correct answer is:
3
3
p : probability of getting head
q : probability of getting tail
Such that, p + q=l
According to question we can get head in 2 nd , 4 th , 6 th ... tail.
Hence required probability = qp(l + q 2 + q 4 + .. .) = 
5pq=2-2q 2
5p(l-p) = 2-2(1 -p) 2
5p-5 P 2 =2-2(1+p 2 -2p)
5p - 5p 2 = 2 - 2 - 2p 2 + 4p
3p 2 =p
p(3p-1).0
p=0, 
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