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jmc

prealgebra senior

Problem

Jar A has exactly four red buttons and eight blue buttons. Carla then removes the same number of red buttons as blue buttons from Jar A and places them in an empty Jar B. Jar A now has of its original number of buttons. If Carla were now to randomly choose a button from Jar A and a button from Jar B, what is the probability that the two chosen buttons will both be red? Express your answer as a common fraction.
Solution
Two-thirds of Jar A's original buttons is 8 buttons. Therefore, four buttons were removed from Jar A: two red buttons and two blue buttons. So the probability that the button drawn from Jar A is red is and the probability that the button drawn from Jar B is red is . Therefore, the probability that both buttons are red is .
Final answer
\frac{1}{8}