Conditional Probabilityhard
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Let X1,X2,X_1, X_2, \dots be a sequence of independent Bernoulli random variables with parameter p(0,1)p \in (0, 1). Let T=inf{n1:Xn=1,Xn+1=1}T = \inf \{n \geq 1 : X_n = 1, X_{n+1} = 1\} be the index of the first occurrence of two consecutive successes. What is the probability that T=3T = 3?