A fair coin is flipped repeatedly until two consecutive heads appear. What is the expected number of flips?
Answer and explanation
Correct answer: B.
- Step 1: Let be expected flips from start. If first flip is T (prob 1/2), cost is .
- Step 2: If first flip is H and second is T (prob 1/4), cost is .
- Step 3: If first flip is H and second is H (prob 1/4), we stop in 2 flips.
- Step 4: Set up equation: .
- Step 5: Expand: .
- Step 6: Solve: .
Answer
6.
Why not the others: '' assumes independent pairs; '' uses ; '' miscalculates intermediate fractions.
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