Let X1 and X2 be independent geometric random variables having the same parameter p. Guess the value of P{X1 = i|X1 +X2 = n}

Hint: Suppose a coin having probability p of coming up heads is continually flipped. If the second head occurs on flip number n, what is the conditional probability that the first head was on flip number i, i = 1, . . . , n −1?
Verify your guess analytically.