A bag contains 3 red chipsand 2 blue chips and one white chip. If two chips are chosen from the bag (without r?
A bag contains 3 red chips and 2 blue chips and one white chip. If two chips are chosen from the bag (without replacement) determine the probability that they are of different colors. Explain.
3 red, 2 blue, 1 white. There is a 1/2 chance that you pick red the first time, 1/3 that you pick blue and 1/6 that you pick white. The same chances apply for the second time so square those values to find the chance that you get that color twice in a row. (1/2)(1/2)+(1/3)(1/3)+(1/6)(1/6) = 1/4+1/9+1/36=7/18. 7/18 is the probability that you get the same color twice in a row. Thus, 1-7/18 is the probability that they are different colors. Thus, 11/18 is your answer.
Oops, I simplified the problem from what it is. I assumed that the you put back the chip that you chose the first time and pick again. As this is not the case, the correct answer would be (3/6)(2/5)+(2/6)(1/4)+(1/6)(0/5)=17/60. Thus, the answer to the question you are asking is really 17/60.
Make sure you understand the question properly. I often mess this up if I don’t read it twice!
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