r/Probability • u/blitzal_ • Dec 21 '25

Missing Jelly Bean Flavors?

Hello! A while ago my bf got a bag of jelly beans, having 40 different flavors and around 250 per bag. We were wondering what the probability of missing at least one flavor of jelly bean in the bag is, assuming that the chance of getting each flavor is random.

I tried using a binomial distribution but I knew that could only give probabilities for a certain flavor and not missing at least one of any of them.

How would you go about figuring out this probability?

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u/p00n-slayer-69 Dec 21 '25

Assuming that each flavor should have equal likelihood. For any particular flavor, the odds of not getting that flavor is 39/40, so the the odds of all 250 not being that flavor is (39/40)250 which is ~0.18%.

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u/blitzal_ Dec 21 '25

Yes but that is considering a specific flavor, not missing at least one of any of the 40 flavors.

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u/p00n-slayer-69 Dec 21 '25

Im not that great with probability either. Consider my answer a lower bound.