##### Need help comparing probability

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Of the 35 students in a class, 22 are taking the class because it is a requirement, and the other 13 because it is an elective. If 2 students are selected at random from this class, what is the probability that the first student is taking the class as an elective and the second student is taking it because it is a requirement? How does the probability compare to the probability that the first student is taking the class because it is a requirement and the second is taking it as an elective?

The probability of two events occurring means you multiply the probabiltiy of one by the other. So if you ever read, "what's the probability of *blank* and *blank*?" then you add the two probabilities. In the event that they are in a particular order, like A and B or B and A, then you will have slightly different calculations. This is because you have decreased the sample size. If you have 10 dice in a bag, and 5 are red and 5 are blue, and you draw a red dice from the bag, there is one less, so the probability of drawing another red has decreased, cause now instead of 5 out of 10, there are only 4 out of 9. The probability of drawing a blue has increased because now instead of 5 out of 10, there are 5 out of 9. It's like that.

So now let's do it in terms of this problem. The probability that the first student is taking the class as an elective is 13 out of 35, which is .37. The probability of the second student taking the class because it's required is 22 out of 34, which is .647.

The probability of this happening in that order is .239.

However the other way around, the probabilities are 22/35= .628 and 13/34= .38 which when multiplied is .238. Not much different but it can be depending on the number you draw out, the amount of each left in the population, and other factors. It also depends on how you round it.

I hope this helps, let me know if I can help you with anything in the future. Take care Robdawg.

-Doctor Turner

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