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
