Balls are chosen at random

In summary, the discussion was about the probability of winning a game in which three different numbers between 1 and 10 are chosen and two balls are picked at random. The given answer was 1/15, but the correct answer is 1/90. This is because the probability of the first ball matching any of the chosen numbers is 3/10 and the probability of the second ball matching any of the remaining numbers is 2/9, resulting in a total probability of 1/15.
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This problem appeared in a problem set which I encountered on the internet

In a game, balls are labeled by integer numbers. One chooses three different integer numbers between 1 and 10. Two balls are picked at the same time, at random from a box. If they are part of the three earlier chosen numbers, the player wins. What's the probability that the player will win?

The given answer is 1/15. But I found 1/90. The probability that the first ball is labeled by one of the chosen numbers is 1/10 and the second is 1/9. And I considered that picking two balls at the same time is equivalent to picking them in sequence. So (1/10) (1/9) = 1/90.
 
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kent davidge said:
The probability that the first ball is labeled by one of the chosen numbers is 1/10
That's the probability that it matches a specific one of the chosen numbers. But there were 3 chosen numbers, so the probability of it matching any of them is 3/10. Likewise, the probability of the second ball matching either of the remaining numbers is 2/9. So the overall probability is 6/90 = 1/15.
 
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  • #3
mjc123 said:
That's the probability that it matches a specific one of the chosen numbers. But there were 3 chosen numbers, so the probability of it matching any of them is 3/10. Likewise, the probability of the second ball matching either of the remaining numbers is 2/9. So the overall probability is 6/90 = 1/15.
Yea, I quickly realized that after my post. (3/10)(2/9) = 1/15.
 

What does "balls are chosen at random" mean?

"Balls are chosen at random" means that the selection process is completely unpredictable and each ball has an equal chance of being chosen. This means that the selection is not influenced by any factors and is purely based on chance.

What is the probability of choosing a specific ball when selecting at random?

The probability of choosing a specific ball when selecting at random depends on the total number of balls and the number of balls of that specific type. For example, if there are 10 balls and 3 of them are red, the probability of choosing a red ball at random is 3/10 or 30%.

Can the same ball be chosen more than once when selecting at random?

Yes, the same ball can be chosen more than once when selecting at random. This is because each selection is independent and the previous selections do not affect the probability of choosing a specific ball in the future.

How does the number of balls affect the randomness of the selection process?

The number of balls does not affect the randomness of the selection process. As long as the selection is truly random, each ball has an equal chance of being selected regardless of the total number of balls.

Are there any strategies for increasing the chances of selecting a specific ball when choosing at random?

No, there are no strategies for increasing the chances of selecting a specific ball when choosing at random. The selection process is completely unpredictable and any attempts to influence it would result in a biased selection.

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