Somnium wrote:

Hello, would much appreciate help with this kind of question :

there are 3 baskets, each with 5 balls.

in first basket we have 4 black balls, 1 yellow.

in second we have 3 black balls, 2 yellow.

in third we have 2 black , 3 yellow.

we pick one ball from each basket. what is the probability that we get at least one black ball ?

thanks

If you see language like 'at least one' in a probability problem, this strategy will usually work. Instead of finding the probability of getting one black ball, then two black balls, then three black balls, you can actually just find the probability of getting all yellow balls, and subtract from 1. You can do that because you're basically looking for the probability that

anything other than all yellow is what happens. That'll be the 'opposite' of the probability that you get all yellow.

The probability of getting all yellow balls is 1/5 * 2/5 * 3/5 (the product of the probability of getting a yellow ball from each basket). That equals 6/125.

So, the probability of getting at least one black (in other words, NOT getting all yellow) is 1-6/125 or 119/125.

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