Question 1196701
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Grammatically, the statement of the problem is flawed.  "If you get the same color twice..." implies that you are doing something twice -- e.g., spinning one of the spinners twice.  But the apparent intent of the question is that EACH spinner is spun ONCE.<br>
Overlooking that shortcoming with the statement of the problem....<br>
Only the red and green colors are on both spinners, so note that the sum of the answers to the two questions must be 1.<br>
Spinner #1 is 1/4 red; spinner #2 is (1/2+1/6) = 2/3 red.  The probability of getting red on both spinners is (1/4)(2/3) = 2/12.<br>
Spinner #1 is 1/2 green; spinner #2 is 1/6 green.  The probability of getting green on both spinners is (1/2)(1/6) = 1/12.<br>
So the probability of getting the same color on both spinners is (2/12)+(1/12) = 3/12.<br>
Then the CONDITIONAL probability that you get red on both spinners, GIVEN THAT you got the same color on both spinners, is (2/12)/(3/12) = 2/3.<br>
And the conditional probability that you get green on both spinners, given that you got the same color on both spinners, is (1/12)/(3/12) = 1/3.<br>
ANSWERS: red 2/3; green 1/3<br>
And note that the sum of the two answers is 1, as it must be....<br>