Eight equal-strength players, including Alice and Bob, are randomly split into 4 pairs, and each pair plays a game (i. e. 4 games in total), resulting in four winners. What is the probability that exactly one of Alice and Bob will be among the four winners

probability that exactly one of Alice and Bob  will be among the winners is 0.5714

Explanation:

The question is to determine the probability that oneof Alice and Bob will be among the winners

It is also important to note that Alice and Bob cannot win at the same time

Therefore,

Probability of Alice and Bob split up = 6/7

Based on this probability, we make the case as follows

First case: Alice wins and Bob loses

Probability of Alice win = 1/2

Probability of Bob lose =                    1

Probability of Alice winning and Bob losing = 1/2 x 1/2 =1/4

Second Case: Bob wins and Alice loses

Probability of Bob win = 1/2

Probability of Alice lose =                    1

Probability of Bob winning and Alice losing = 1/2 x 1/2 =1/4

Third Case

The Probability that Alice and Bob play each other = 1/7

Based on all the estalished Cases

The required probability that exactly one of Alice and Bob  will be among the winners is

(6/7 x 1/4) + (6/7 x1/4) + 1/7

= (2 x 6/7 x 1/4) + 1/7

= 6/14 + 1/7

= 3/7 +1/7

= 4/7 = 0.5714                                                  

the correct answer is economics is a game without winners or losers.

unlike sports or games economic is a game without losers or winner rather it is a game where everyone wins. parties of business doing businesses exchange money with each other and hence exchange is done on the basis of goods. one party takes the goods and other sales it so there is winner on both sides. each party values more highly the good it gets than the good it gives up. both sides exchange only because both intend to increase their value. so there is no concept of lose or win.