Discrete Probability: Below is the problem and make sure to show the full and correct solution:    Peter has probability 2/3 of winning each game. Peter and Paul bet $1 on each game. If Peter starts with $3 and Paul starts with $5, find the expected number of games played until someone goes broke.

Karey has three movie choices. She can choose between a comedy, a drama, or a thriller. She will want a snack as well. Her choices are popcorn, nachos & cheese, potato chips, or peanuts. What is the probability that she will watch a thriller and eat popcorn?

maya is playing a role playing game with her friends. She will roll a dice to determine if her character casts a spell. The odds in favor of her character casting a spell are 8/7.  Find the probability of her character casting a spell.