Answer:
$1.68 per match
Average Fee = $1.69
Step-by-step explanation:
Given:
- Earnings for all 3 different number = $ 1
- Earnings for 2 same number = $ 2
- Earnings for 3 same number = $ 6
- Five sided fair dice = 3
Find:
- Expected pay-out
- What fee charged per match for 10 cent income
- Reason for change to new match
Solution:
- Construct a probability distribution table, where X: payout per match
X $1 $2 $6
P(X) 0.48 0.48 0.04
Case X = $1 : _ _ _ All three different numbers
No.outcomes 5 * 4 * 3 = 60
Total outcome 5 * 5 * 5 = 125
Hence, P(X= $ 1) = 60 / 125 = 0.48
Case X = $2 : S _ S two numbers are same
No.outcomes = 5 * 4 * 1 = 20 per combination
Total combinations = S _ S + S S _ + _ S S = 3
Total outcome = 3 * 20 = 60
Hence, P(X= $ 2) = 60 / 125 = 0.48
Case X = $6 : S S S two numbers are same
No.outcomes = 5 * 1 * 1 = 5 per combination
Total combinations = 1
Total outcome = 5 * 1 = 5
Hence, P(X= $ 2) = 5 / 125 = 0.04
- Expected Payout E(X):
E(X) = 1*0.48 + 2*0.48 + 6*0.04 = $1.68 per match
- To earn $0.01 on average the fee of match is:
Fee_avg = E(X) + $0.01 = $1.69
- With this new plan your friend would loose less. The expected payout of a match is $1.68 for which the probability X < $ 2 is around = 0.48. However, to gain a $2 or higher P ( X > 2 ) = 0.48 + 0.04 = 0.52. Hence, the week-payout for X > 2 is greater than 7*2 = $14. So probability of week's payout to be $14 is higher than to be $ 11.76 as per average pay per day.
