There are eight balls in an urn. They are identical except for color. Four are r

Question

There are eight balls in an urn. They are identical except for color. Four are red, three are blue, and one is yellow. You are to draw a ball from the urn, note its color, and set it aside. Then you are 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 ball 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

Number of outcomes = 8*7=56

P(R, R) = 4 * 3 /56 = 12/56

P(R, B) = 4*3 /56=12/56

P(R, Y) =4 * 1 = 4/56

P(B, R) = 3*4 = 12/56

P(B, B) =3*2 = 6/56

P(B, Y) = 3/56

P(Y, R) = 4 /56

P(Y, B) = 3/56

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