Question

A coin that when flipped comes up headswith probability p until either heads or tails has occured twice. Find the expected number of flips

Answer 1

Answer:

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Step-by-step explanation:

I can't understand your question ????

Answer 2

Answer: 3 - p^2 - (1 - p)^2

Step-by-step explanation:

Its not necessary to be consecutive, so at max we need 3 flips and minimum 2 flips. So

X = 2, 3

If probability of getting head is p,

Then probably of getting tail is (1-p)

So, P(X=2) = 2H or 2T = p^2 + (1-p)^2

Again,

P(X=3) = 1 - P(X=2) [since only 2 random variables]

P(X=3) = 2p(1-p)

Now,

E(X) = 2P(X=2) + 3P(X=3)

= 3 - p^2 - (1-p)^2