perplexus.info :: Probability : Colored Marble Muse

Colored Marble Muse (Posted on 2022-05-07)

Saul, Simon and Stuart each have a bag containing 5 different colored marbles. Each bag contains the same five colors.
o Saul reaches into Simon's bag and Stuart's bag and randomly withdraws a marble from each and places them in his bag.
o Simon then reaches into Saul's and Stuart's bag and randomly withdraws a marble from each and places them in his bag.
o Finally, Stuart reaches into Saul's and Simon's bag and randomly chooses a marble from each and places them in his bag.
Determine the probability that each of the three boys has five different colors of marbles in their bag.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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re: Solution by cases

| Comment 3 of 4 |

(In reply to Solution by cases by Jer)

If this helps:

I ran the program keeping track of only your two cases: the first player chose the fifth color from each of the second player and the thrid player; and the first player chose color 5 from the second and color 4 from the third.

The former had 48 successes out of 1008 cases; the latter had 40 successes out of its 1008 cases. The reduced fractions are 1/21 and 5/126.

The former contributes 1/5 of the 1/21, making 1/105, and the latter 4/5 of 5/126, making 2/63.

then 1/105 + 2/63 = 13/315.

Posted by Charlie on 2022-05-07 23:03:13

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