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Three children, John, Paul, and Ringo, are playing a game. Each child
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25 Oct 2021, 05:42
25 Oct 2021, 05:42
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15% (01:42) correct
85% (01:31) wrong based on 40 sessions
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Three children, John, Paul, and Ringo, are playing a game. Each child will choose either the number 1 or the number 2. When one child chooses a number different from those of the other two children, he is declared the winner. If all of the children choose the same number, the process repeats until one child is declared the winner. If Ringo always chooses 2 and the other children select numbers randomly, what is the probability that Ringo is declared the winner?
A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 2/3
A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 2/3
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Joined: 10 Apr 2015
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Re: Three children, John, Paul, and Ringo, are playing a game. Each child
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25 Oct 2021, 06:01
25 Oct 2021, 06:01
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Carcass wrote:
Three children, John, Paul, and Ringo, are playing a game. Each child will choose either the number 1 or the number 2. When one child chooses a number different from those of the other two children, he is declared the winner. If all of the children choose the same number, the process repeats until one child is declared the winner. If Ringo always chooses 2 and the other children select numbers randomly, what is the probability that Ringo is declared the winner?
A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 2/3
A. 1/6
B. 1/4
C. 1/3
D. 1/2
E. 2/3
This is one of my all-time favorite questions!!
The main concept here is that all 3 children are equally likely to win this game (unless one of them possesses supernatural powers that allow him to know what numbers the other two boys will choose
)Also note that, if everything is random, the probability of winning by choosing the number 2 is the same as the probability of winning by choosing the number 1.
So, regardless of what number Ringo chooses, his probability of winning is exactly the same as each of the other boys winning.
Since all 3 boys have the same probability of winning, P(Ringo wins) = 1/3
Likewise, P(John wins) = 1/3 and P(Paul wins) = 1/3
Answer: C
Cheers,
Brent
Re: Three children, John, Paul, and Ringo, are playing a game. Each child
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28 Sep 2024, 22:23
28 Sep 2024, 22:23
1
Make a table:
J P R(fixed =2)
1 2 2
2 1 2
1 1 2
john wins = 1/3
paul = 1/3
ringo 1/3
J P R(fixed =2)
1 2 2
2 1 2
1 1 2
john wins = 1/3
paul = 1/3
ringo 1/3
