In a certain two-dice game, you win 4 dollars if a prime number of dots appear. Otherwise you lose 1 dollar. What is the approximate expected value of the payoff?
1 Answer
Aug 5, 2017
Explanation:
The possible prime numbers that can occur are:
-
#2# in#1# way, namely#1+1# -
#3# in#2# ways, namely#1+2# ,#2+1# -
#5# in#4# ways, namely#1+4# ,#2+3# ,#3+2# ,#4+1# -
#7# in#6# ways, namely#1+6# ,#2+5# ,#3+4# ,#4+3# ,#5+2# ,#6+1# -
#11# in#2# ways, namely#5+6# and#6+5#
That makes
It leaves
So the expected value of the payoff is:
#4*15/36-1*21/36 = (60-21)/36 = 39/36 = 13/12# dollars
