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raketka [301]
3 years ago
6

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
Business
1 answer:
Minchanka [31]3 years ago
8 0

Answer:

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                                                  

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July 31 Fees Earned                    520,400    

               Wages Expense                          488,000  

               Rent Expense                                    65,000  

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               Miscellaneous Expense             13,900  

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Marlena Fenton, Drawing = $11,000

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