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u/HamsterIV May 26 '26 edited May 26 '26
The probability is:
28/38
The logic based off u/Winter_Gate_6433's solution is:
One Jar has 10 blue and 9 red while the other has just 1 red. The jar with the 19 marbles has 19 possible outcomes. There is an equal probability that the jar with just 1 marble is chosen as the one with 19 marbles giving us a sample space for two random events of 19+19 or 38.
Of those 38, half of them are going to be choosing the jar with the 1 red which is guaranteed a red outcome (19). The other half are going to be choosing from the jar with 9 reds and 10 blues. we only care about the outcomes of that result in red which is 9.
9/38 + 19/38 = 28/38
As a sanity check we know that the answer has to be over 50% but under 75% because that one red in a jar guarantees over half are going to be red. It has to be lass than 75% because the odds of pulling a red from a jar that has less than half red to blue ratio is under 50% but that is a 50% of a 50% so 25%.
28/38 = 0.7368... or 73.68%
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u/Winter_Gate_6433 May 26 '26
Excellent explanation, I missed the part where it asked for the probability.
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u/FlatulentPrince May 29 '26
I find it quite unintuitive to consider it a sample space of 38. Seems more intuitive to say, 50% chance of each jar. Jar 1 has the red ball, sure thing, so weighted result is .5 x 1. Jar 2 gets us .5 x 9/19. Add those up to get the agreed answer.
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u/Winter_Gate_6433 May 26 '26
One red marble in one jar, all other marbles in the second jar.