The following dice game is offered to you. You may simultaneously roll one red die and three blue dice. The stake is $1. If none of the blue dice matches the red die, you lose your stake; otherwise, you get anyway paid k +1 dollars if exactly k of the blue dice match the red die. In the case that exactly one blue die matches the red die, you get paid an additional $0.50 if the other two blue dice match. the median payoff of the game is

In American roulette, the wheel contains the numbers 11 through 3636, alternating between black and red. There are two green spaces numbered 00 and 0000. A player places a bet of $0.50$⁢0.50 on red to play the game. If the ball lands on red, the player gets a $0.50$⁢0.50 for winning and receives the money back. If the ball does not land on red, then the player simply loses the $0.50$⁢0.50 placed on the bet. If the player places the same bet on red 99 times, what is the player’s expected winnings? Round your answer to the nearest cent.

Last semester in a business fraternity, 30% of the members were on the Dean's List and 15% of the members were on academic probation.  If being on the Dean's List and being on academic probation are mutually exclusive events, find the percent of members who were neither on the Dean's List nor on academic probation.

If you roll two dice, each with 8 faces,  what sum is most likely to appear from the two dice?   Write out each step and explain what you are doing in each step.

A player pays a certain amount of money to randomly roll a 6-sided and a 4-sided die, both balanced. If the sum of the dice is less than 5 or greater than 9, the player receives a prize of $ 90. Otherwise he loses the money paid to play, in dollars and cents, to keep this game fair. Write only the number corresponding to the prize without a dollar sign and rounded to 2 decimal places.

In a lottery, the top cash prize was $646 million, going to three lucky winners. Players pick four different numbers from 1 to 57 and one number from 1 to 47. A player wins a minimum award of $200 by correctly matching two numbers drawn from the white balls (1 through 57) and matching the number on the gold ball (1 through 47) What is the probability of winning the minimum award?

A child rolls 7 standard dice of different colors and records the numbers showing. Find the number of different outcomes

During his short stint as Shadow Finance Minister, Barnaby Joyce displayed a curious grasp of numbers. One of his most infamous exclamations was “All this billions, quillions, Brazilians.” Less well known was his tax-reform proposal, recommending that if you earn $x per day, you are taxed x% of that amount (with the understanding that you pay 100% tax if you earn $100 or more per day. Under Senator Barnaby’s plan, which amount x gives you the highest earnings after tax has been taken out?

A restaurant will select one card from a bowl to win a free lunch.Jimmy puts 10 cards in a bowl. the bowl has a total of 150 cards in it when they do not when they do the drawing what are the odds of Jimmy winning a free lunch?