Question #$2$: Gambling in Sports $[22$ Points$]$

When a casino accepts a point spread bet, it gives the payer the odds of $10$ to $11.$ In other words for every

$$11$ dollars the player wagers, the player will win $$10.$ Suppose that the Mandalay Bay Casino has

collected bets on the New York Knicks $-$ Boston Celtics game. The Celtics are favored by $8$ points over

the Knicks.

$($a$)$ Suppose that the casino has collected a total of $$19,470$ in wagers on the game and gamblers have bet

equal sums on both sides. $$9735$ has been bet on the Celtics and $$9735$ has been bet on the Knicks. If the

final score of the game is Celtics $98$ and Knicks $104$ how much profit will the casino earn?

$[8$ Points$]$

$($b$)$ Suppose that the casino has collected a total of $$19,470$ in wagers on the game but gamblers have not

equal sums on both sides. Suppose that $$13,629$ has been bet on the Celtics and only $$5,841$ has been bet

on the Knicks.

$($i$)$ Calculate the casino's profit if the final score is the Celtics $94$ and Knicks $90.[7$ Points$]$

$($ii$)$ Calculate the casino's profit if the final score is the Celtics $101$ and Knicks $80.[7$ Points$]$