Question

A modified roulette wheel has 36 slots. One slot is 0, another is 00, and the others are numbered 1 through 34, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd or even.)a. what is the probability of winning______b. what is the actual odds against winning? _____:______c. when you bet that the out come is an odd number, the payoff odds are 1:1 how much profit do you make if you bet $15 and win?d. if you win the pay off is $______

Answer 1

a) 17/36

b) 19/17

c) $15

d) $30

Explanation:

Total number of slots, n : 36

Number either even nor odd, : 2

Even numbers will be:

{2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34}= 17

Odd numbers: {1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33}= 17

a) placing a bet an outcome is an odd number:

Probability of winning=

(Odd numbers/ total number

= 17/36

b) actual odds against winning=

Ways of losing/ways of winning

= 19/17

c) since the payoff odd is 1:1 and I staked $15, it means I will have a profit of $15 if I win. 1:1 means your profit will equal your stake.

To calculate, we use

(a*c)/b

Here,

a : b = payoff odds

c = stake

We have:

(1*15)/1 = $15

d) Hence, if I win, the payoff would be:

$15+$15 = $30

Answer 2

Explanation:

Consider the provided information.

It is given that the modified roulette wheel has 36 slots {0,00,1...34}

You are placing a bet that the outcome is an odd number.

The odd number from 1 to 34 is 17.

Part (A)

The probability of winning is:

`Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}`

`P (Win)=(17)/(36)`

`P (Win)=0.472`

Hence, the number of probability of winning is 0.471

Part (B)

The actual odd against winning is:

Odd against = Way to lose : Way to win

As we know way to win are 17, thus the way to lose are 19.

Odd against = 19 : 17

Hence, the odd against is 19:17.

Part (C)

If you bet $15 that the out come is an odd number, the payoff odds are 1:1.

Here, 1:1 means that you will get a profit of $1 for every $1 of bet.

So, if the bet is $15 then the profit will be $15.

Hence, the profit do you make if you bet $15 and win $15.

Part (D)

Now we need to find pay off if you win.

The payoff will be $15+$15=$30

If you win the bet then the payoff will be the $30.