Question

A game of chance involves rolling a 15-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 8 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings?

Answer 1

solution:

total possible outcome in rolling a 15 sided dice = 15

for winning 2 dollor

number of ways of rolling 1 to 3 (1 or 2 or 3) = 3 ways

probability of rolling 1 to 3 = 3/15

for winning 8 dollor

number of ways of rolling 4 or 5 = 2 ways

so probability of rollilng 4 or 5 = 2/15

for none winning

number of ways of rolling 6 to 15 = 10

probability of rollling 6 to 10 = 10/15

so payment for a play = $5

probability distribution of winning is

win(X)	prob.(X)
$2	3/15
$8	2/15
$0	10/15

so expected winning =

so expected winning = - $3.53

it is an expected loss of $ 3.53