There are ten balls in an urn. They are identical except for color. Four are red
ID: 3239597 • Letter: T
Question
There are ten balls in an urn. They are identical except for color. Four are red, five are blue, and one is yellow. You are to draw a ball from the um, 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) = 3/28 P(R, B) = P(R, Y) = P(B, R) = P(B, B) = P(B, Y) = P(Y, R) = P(Y, B) =Explanation / Answer
Drawing two red balls:
For first draw we have 10 balls out of which four are red so
P(first red) = 4/10
For second draw we have 9 balls out of which 3 are red so
P(second red | first red) = 3/9
So
p(R,R) = P(second red | first red)P(first red) = (3/9)*(4/10) = 12/90
-----------------
Likewise
p(R,B) = P(second blue | first red)P(first red) = (5/9)*(4/10) = 20/90
p(R,Y) = P(second yellow | first red)P(first red) = (1/9)*(4/10) = 4/90
p(B,R) = P(second red | first blue)P(first blue) = (4/9)*(5/10) = 20/90
p(B,B) = P(second blue | first blue)P(first blue) = (4/9)*(5/10) = 20/90
p(B,Y) = P(second yellow | first blue)P(first blue) = (1/9)*(5/10) = 5/90
p(Y,R) = P(second red | first yellow)P(first yellow) = (4/9)*(1/10) = 4/90
p(Y,B) = P(second blue | first yellow)P(first yellow) = (5/9)*(1/10) = 5/90