Probability Distribution problem. How would I set this up, and what formulas?

A single die is rolled once. You lose $12 if a number divisible by 3 turns up. How much should you win if a number not divisible by 3 turns up for the game to be fair? How would I set this up, and what formulas?

Complement of Events, Guessing. How do I setup a Guessing problem?

Six popular brands of cola are to be used in a blind taste study for consumer recognition. A. If 3 distinct brands are chosen at random from the 6 and if a consumer is not allowed to repeat any answers, what is the probability that all 3 brands could be identified by just guessing? B. If repeats are allowed in the 3 brands chosen at random from the 6 and if the consumer is allowed to repeat answers, what is the probability of correct identification of all 3 by just guessing?

Markov Chains - Need help with problem layout, formulas and setup.

Text does not provide very good information on Markov Chains. Consumers in a certain area can choose between three package delivery services: APS, GX, and WWP. Each week, APS loses 10% of its customers to GX and 20% to WWP, GX loses 15% of its customers to APS and 10% to WWP, and WWP loses 5% of its customers to APS and 5% to GX. Assuming that these percentages remain valid over a long period of time, what is each company's expected market share in the long run?

Markov Chains - Scheduling problem, Need help with setup of problem.

An outdoor restaurant in a summer ersort closes only on days that it rains. From past records it is found that from May through September, when it rains one day, the probability of rain for the next day is .6; when it does not rain one day, the probability of rain the next day is .1. A. Draw a transition diagram. (????) B. Write the Transistion Matrix. C. If it rains on Thursday, what is the probability that the restaurnat will be closed on Saturday? And on Sunday?

Probability, How do you set this up using probability distribution table?

In a family with 2 children, excluding multiple births and assuming that a boy is as likely as a girl at each birth, what is the expected number of boys?