Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I've been working on a little side project, but I've hit a road block on the maths for this one. Basically if you imagine a sealed pack of 10 cards, there is a 20% chance that the pack contains one foil (more valuable) card. The mass distribution of the foil cards are (heavier and) different to the non-foil equivelant.

What I would like to do, is calculate the probability of a sealed pack containing a foil card, given the mass of the pack. Essentially I have 3 normal mass distributions for the non-foil cards, foil cards, and packaging. The next step is to combine the 3 normal distributions to give me a bell-curve that shows the probability of a pack containing a foil, given a mass.

I'm guessing I would need to find the product of the packaging, 9 non-foil cards, and 1 foil card distribution; I've struggled to find information on how to do this. Any guidance, or thoughts on this would be most appreciated!

Thanks,

Charij

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# Finding the product of multiple normal distributions

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