Question

$ (prize)	$(profit)	x = # of heads	P(x)
$1	$3	0	0.03125
$ 1	$3	1	0.15625
$1	$ 1	2	0.31250
$1	$1	3	0.31250
$ 1	$0	4	0.15625
$ 1	$0	5	0.03125

1. A fair coin is tossed five times. The probability of observing “x” heads among the 5 coins is given in the table above. A particular game consists of tossing a fair coin 5 times. It costs $1 to play the game; you win $3 if 0 or 1 heads turn up, you win $1 if 2 or 3 heads turn up and you win nothing if 4 or 5 heads turn up.

a. Find the expected number of heads.

b. Find the expected value of your prize. (This ignores the cost to play.)

c. Find the expected value of the profit. (This includes the cost to play.)

d. Is the game in your (the player) favor, or in the favor of the “house”?

Answer 1