There are nine balls in an urn. They are identical except for color. Four ne red

Question

There are nine balls in an urn. They are identical except for color. Four ne red, four are blue and one is yellow. You are to draw a ball from the urn, note its color, and set it aside. Then you re to draw another ball from the urn and note its color. (a) Make a tree diagram to show all possible outcomes of the experiment. (b) Let P(x, y) be the probability of choosing an x-colored ball on the first draw and a y-colored bell on the second draw. Compute the probability for each outcome of the experiment. (Enter your answers as fractions.) P(R, R) = P(R, B) = P(R, Y) = P(B, R) = P(B, B) = P(B, Y) = P(Y, R) = P(Y, B) =

Explanation / Answer

a) Option B (Top right) graph is correct. Because in second draw, there must be two three branches and one two branches

b) P(R,R) = 4/9*3/8 = 1/6

P(R,B) = 4/9*4/8 = 2/9

P(R,Y) = 4/9*1/8 = 1/18

P(B,R) = 4/9*4/8 = 2/9

P(B,B) = 4/9*3/8 = 1/6

P(B,Y) = 4/9*1/8 = 1/18

P(Y,R) = 1/9*4/8 = 1/18

P(Y,B) = 1/9*4/8 = 1/18

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