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Probability of choosing a blue counter = 4/(4+8)



Not replacing the blue counter then the probability of choosing an yellow counter = 8/(8+3)


One of the easiest ways to find this is by drawing a probability tree diagram. There would be two different branches: the first branch being the first ball picked out, and the second would be the second ball picked out without the first being replaced. The probability of picking out a blue counter the first time would be 4/12 since there are 12 counters in total and 4 of them are blue. 8/12 would be the probability of picking a yellow counter since there are 8 yellow counters. Then we move onto the second branch after we have already picked a blue counter. Since we have not replaced the first counter, there are now 11 counters in the bag, 3 of which are blue since one was already taken out, and 8 of which are yellow from before. This means the probability of a yellow counter in the second pick is 8/11. We now multiply both the probabilities, the probability of a blue counter the first time and a yellow counter in the second pick which would be 4/12 x 8/11 = 32/132. This can then be simplified by dividing both the numerator and denominator by 4 giving us 8/33. 

How this works is when a variance of probability isn't replaced then it reduces total fractional amount as a probability.

So the first trial would be 4/12=blue
(12 because the total units involved is 12)
This can be simplified as 1/3 one third

Since is it not replaced then the total amount will decrease as well as the variant deducted.

So the second trial would be 8/11=yellow

Strangely enough this increases the probability of the yellow because there are less variables.

To complete the process you need to connect these two trials together, this is where you would multiply.

4/12 x 8/11 = 32/132 you would simplify this by dividing by the highest that can go into the numerator and the denominator which is 4 = 8/33 this would be your final answer.

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