A modified roulette wheel has 32 slots. one slot is 0, another is 00, and the others are numbered 1 through 30, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /> a. What is your probability of winning ?

The probability of winnign is ?

( type an integer or a simplified fraction)

b. What are the actual odds against winning are ?

c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $17 and win ?

If you win, the pay off is ?

d. How much profit should you make on the $17 bet if you could somehow convice the casino to change its payoff odds so that they are the same as the actual odds against winning ?

(rounds to the nearest cent as needed.)Type your question here

0.46875 ; 1.133 ; $17 ;19.27

Step-by-step explanation:

Number of slots = 32

0, 00, {1,.. 30}

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

1.) probability of winning :

P(winning) = number of odd outcomes / tot possible outcomes

P(winning) = 15 / 32 = 0.46875

2.)

Odds against winning :

Number of losing outcomes / number of winning outcomes

Not odd numbers / odd numbers = 17 /15 = 1.133

C.)

Payoff odd = 1:1

If bet value = $17 ;

Profit made on winning = $17 * 1 = $17

d.)

If Payoff odd = odd against winning = 17 / 15

Profit on $17

17/ 15 * 17

(1.1333333) * 17

= 19.27

;

Both f(g(x)) and g(f(x)) are equal to simply x. This is because these two equations are inverse equations.

To find each of these composites, take the original equation and plug the other in for the x term. For f(g(x)) we start with the f(x) equation and then put g(x) in for x.

f(x) = -4x + 60 > Plug g(x) in for x

f(g(x)) = -4(-1/4x + 15) + 60 > Distribute the -4

f(g(x)) = x - 60 + 60 > Simplify

f(g(x)) = x

Then we can check the other in the opposite order.

g(x) = -1/4x + 15> Plug in f(x) for x

g(f(x)) = -1/4(-4x + 60) + 15 Distribute the -1/4

g(f(x)) = x - 15 + 15 > Simplify

g(f(x)) = x

And if both are equal to x, this means they are inverse functions.