In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00. a.) Find the probability of winning if you pick the number 7 and it comes up on the wheel. b.) Find the odds against winning if you pick the number 7. c.) The casino will pay you $20 for every dollar you bet if your number comes up. How much profit is the casino making on the bet

a) p=0.026

b) q=0.974

c) The casino has a long-run expected profit of $0.43 per bet.

Step-by-step explanation:

a) We have a roulette with 38 slots (37 numbers from 0 to 36, plus the double-0). Then, the probablity of winning if you pick on number (in this case, 7 for instance), can be calculated as the quotient between 1 and 38:

b) The odds against winning, in the case of only picking one slot, is 37 out of 38. Is the complement of the pobability calculated in point a.

c) In this case, we have to calculate the expected value of a game where if our number comes up, we get $20, and if it is not, we lose $1.

This can be calculated as the sum of the outcomes multiplied by its probabilties:

With this result, we can conclude that the casino has a long-run expected profit of $0.43 per bet.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: