Probability

Three friends play a game of darts until one of the 3 is declared a winner. It is known that Jan is twice as likely to win as Julio, and Jean is only half as likely to win as Julio. (a) What is the probability that Julio will win? (b) If Jan didn't win, what is the probability that Julio did?

Probability : Sampling Without Replacement - Card Hands

6. A hand of 4 cards contains one card of each suit ( I,e., one Heart, one Diamond, One Club and one spade). Simon uses this hand to play a game for which the rules are as follows: (1) When a Heart is drawn, the game stops immediately. (2) If the Diamond is drawn, the Diamond is set aside and not replaced (so that when the game ...continues

Probability distribution

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 ...continues

Markov Chains - Scheduling problem

An outdoor restaurant in a summer resort 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 ...continues

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?

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

If the probability distribution for the random variable X is given in the table, what is the expected value of X?

Probability and Random Selection (4 Problems)

A 4 person grievance committee is to be composed of employees in 2 departments, A and B, with 15 and 20 employees, respectively. If the 4 people are selected at random from the 35 employees, what is the probability of selecting: A. 3 from A and 1 from B? B. 2 from A and 2 from B? C. All from A? D. At least 3 from A? ...continues

In a game of dice, find the expected value.

On three rolls of a single die you will lose $10 if a 5 turns up at least once, and you will win $7 otherwise. What is the expected value of the game?

Markov Chains

All welders in a factory begin as apprentices. Every year the performance of each apprentice is reviewed. Past records indicate that after each review, 10% of the apprentices are promoted to professional welder, 20% are terminated for unsatisfactory performance, and the remainder continue as apprentices. A. Draw a transitio ...continues