MathDB

Define the Fibonacci numbers via

F_0=0

f_1=1

, and

F_{n-1}+F_{n-2}

.
Olivia flips two fair coins at the same time, repeatedly, until she has flipped a tails on both, not necessarily on the same throw. She records the number of pairs of flips

c

until this happens (not including the last pair, so if on the last flip both coins turned up tails

c

would be

0

). What is the expected value

F_c

Problem Statement