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URL:  https://boards.fool.com/there-are-3-dice-in-a-bag-6-sided-12-sided-and-34612559.aspx

Subject:  Re: Probability problem Date:  9/8/2020  9:31 AM
Author:  bighairymike Number:  5995 of 6013

There are 3 dice in a bag: 6-sided, 12-sided and 20-sided. We pick one die at random, roll it, and it gives us a number N. What's the probability that when we pick another die and roll it, we'll get a number smaller than N, if N = 4?

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OK, I'll take a crack at it....

Possible scenarios.

1. pull 6 side first which shows the 4, leaves 32 (12+20) possible outcomes in the bag.
2. pull 12 side first which shows the 4, leaves 26 (6+20) possible outcomes in the bag.
3. pull 20 side first which shows the 4, leaves 18 (6+12) possible outcomes in the bag.


So there a universe of 76 total outcomes.

With two dice left in the bag, there are three outcomes less than 4 on each dice, so 6 potential outcomes less than 4.

With three scenarios, each having six potential outcomes less than 4, gives 18 total outcomes less than 4.

18/76 = 0.236842
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