- #1

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## Main Question or Discussion Point

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.

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.