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Consider a box that contains 14 red balls, 12 blue balls and 9 yellow balls. A ball is drawn at random and the color is notef and then put back inside the

box. then, another ball is drawn at random. Find the probability that:
a. Both are blue
b.the first red and the second is yellow


This problem is familiarly known as the "probability of independent events."
a. Let A= the event that the first ball is blue, and B= the event that the second ball is blue.
In the beginning, there are 35 balls in the box, 12 of which are blue. Therefore, expressing it into a probability form as P(A)= \frac{12}{35} .
After the first selection, the ball was returned to the box making the number of balls in the box still equal to 12 blue, 14 red, and 9 yellow balls. So P(B|A)= \frac{12}{35} .
Thus, multiplying the two probabilities yields
P_A_a_n_d_B= \frac{12}{35}( \frac{12}{35} )= \frac{144}{1225}=0.11755

b. Let A= the event that the first ball is red, and B= the event that the second ball is yellow.
Again there are 35 balls, 14 of which are red: P(A)= \frac{14}{35}
For the second selection to be a yellow ball (as which the returning of the first ball to the box is allowed), P(B|A)= \frac{9}{35}
Thus, P_A_a_n_d_B= \frac{14}{35}( \frac{9}{35} )= \frac{18}{175}=0.10286

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