Question

A spinner has eight equally spaced sectors labelled from 1 to 8.  In a particular game, a player wins points equal to double the sector’s face value if a power of two is spun.  For all other spins, the player loses the face value of the spin. is this a fair game? calculate the expectation

Answer 1

1,2,4 and 8 are power of two, thus player wins 2,4,6 and 16 respectively if 1,2,4 and 8 are spun respectively

Each of the 8 sectors can be spun with equal probabilities of 1/8

Expected value of the game

= (1/8)*{1*2 + 2*2 + (-3) + 4*2 + (-5) + (-6) + (-7) + 8*2}

= 9/8 = 1.125

Since, the expectation is not zero, this is not a fair game