Please specify the terms you use (if necessary) and explain each step of your solutions.

In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly, he wins an amount (in dollars) equal to the sum of the fingers shown by him and his opponent. If both players guess correctly or if neither guesses correctly, then no money is exchanged. Consider a specified player and denote by X the amount of money he wins in a single game of Two-Finger Morra.

(a) If each playesr acts independently of the other, and if each player makes his choice of the number of fingers he will hold up and the number he will guess that his opponent will hold up in such a way that each of the 4 possibilities is euqally likely, what are the possible values of X and what are their associated probabilities?

(b) Suppose that each player acts independently of the other. If each player decides to hold up the same number of fingers that he guesses his opponent will hold up, and if each player is equally likely to hold up 1 or 2 fingers, what are the possible values of X and their associated probabilities?

Q. The 'cup' system for determining the champion amongst 2^n players consists of drawing lots to arrange the players in 2^n-1 pairs who are to play each other, then repeating this with the 2^n-1 winners of these matches, and so on. The winner and loser of the final match recieve the first and second prizes repectively.
Suppose

14. A parallel system functions whenever at least one of its components works. Consider a parallel system of n components and suppose that each component independently works with probability ½. Find the conditional probability that component 1 works given that the system is functioning.

Doomsday Airlines ("Come Take the Flight of Your Life") has two dilapitated airplanes, one with two engines, and the other with four. Each plane will land safely only if at least half of its engines are working. Each engine on each aircraft operates independently and each has probability p = 0.4 of failing. Assuming you wish

A student applies for two different scholarships. The probability of receiving the first scholarship is 0.3 and the probability of receiving the second is 0.4. The decisions are made independently. Find the probability the student receives exactly one scholarship.
A. 0.12
B. 0.42
C. 0.46
D. 0.40

Two components of a machine work independently. The probability that component A will fail is 0.1, and the probability that component B will fail is 0.2.
A) What is the probability that both components will fail?
B) What is the probability that only one of the components will fail?
C) What is the probability that at least o

The Question is:
In the game of bridge, each of 4 players is dealt 13 cards. If a certain player has no aces, find the probability that that person's partner has:
a.)no aces
b.)at least 2

((Essentials of Statistics for Business and Economics 6th Editionin)) In Chapter 5 Problem 33
33. 12 of the top 20 finishers in the 2009 PGA Championship at Hazeltine National Golf Club in chcaska, Minnesota used a Titleist brand golf ball (GolfballTest website, November 12, 2009.) Suppose this results are representaive of t

Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue a warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questi

A person tried by a 3-judge panel is declared guilty if at least 2 judges cast votes of guilty. Suppose that when the defendant is in fact guilty, each judge will independently vote guilty with probability 0.7. whereas when the defendant is, in fact, innocent, this probability drops to 0.2. If 70 percent of defendants are guilty