Question

After losing his blackjack game, Ebert then goes to the race track. He wants to bet $20 on one of the following horses:

Horse name Odds Against

Maximum 8:1

Improbable 5:1

Code of Honor 12:1

Game Winner 9:2

Tax 20.1

A)Using the odds given, calculate the probability of each horse winning the race.

B)Based on your calculation in part (a), which horse should ebert bet on? Why?

C) at a horse race, if the odds against your horse are a:b this means that for each $b you bet on the horse, you gain $a if you win. If Ebert bets $20 on the horse you chose for part b, how much will he gain if the horse wins?

D) Use your answer to part (C) to help calculate the expected value of your chosen horse bet? Show calculations, state your answer, and explain in a sentence what your expected value means.

Answer 1

A)

if odds aginst are a:b then probability of winning = b/(a+b)

probability of winning of each horse :

Maximum = 1/(1+8) = 1/9

Improbable = 1/(1+5) = 1/6

Code of Honour = 1/(1+12) = 1/13

Game Winner = 2/(2+9) = 2/11

Tax = 1/(20+1) = 1/21

B)

after looking at probability of winning of each horse

the highest probability of winning is of Game Winner so, Ebert should bet on Game Winner

C)

odds aginst Game Winner = 9:2

on betting $2 you get $9

therefore on betting $20 you get : $20 * (9/2) = $90

D)

on winning profit = $90-$20 = $70

P(winning) = 2/11   {from part a}

on loosing loss = $20

P(loosing) = 1-P(winning) = 1 - 2/11 = 9/11

E(value) = sum of prize*P

= $70 * (P(winning)) + (-$20) * P(lossing)

= 70*2/11 - 20*9/11 dollars

= -3.6363 dollars

the expected value is -3.6363 dollars this means that if you bet $20 you are expected to loose 3.6363 dollars on average