There·re eight balls in an um. They &re; dentical except for color, Tro are red,

Question

There·re eight balls in an um. They &re; dentical except for color, Tro are red, five are blue, end one is yellow. You are to draw 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 Px, )be the probability of choosing an*-colored ball on the first draw and a y-colored ball on the sacond draw. Compute the probability far ach outcome of the exparment. (Enter your answers as fractions.) PÍR, R) - PIR, B) P(R, - P(B, R) P(B, 8) P(B, n

Explanation / Answer

A) Tree diagram - for the firt ball, there are 3 choices. For the second ball, three choices are there if the first ball was red or blue. If first ball was yellow, then the second ball can be either red or blue, not yellow. So, there will be three brances for first ball and for two of thre three branches, there will be 3 sub branches and for one, there will be only 2 sub branches. Such an option is tree diagram 4.

B) P(R,R) = P(drawing a red from the total 8 balls, of which 2 are red) x P(drawing a red from the remaining 7, of which one is red)

= 2/8 x 1/7

= 1/28

P(R,B) = 2/8 x 5/7

= 5/28

P(R,Y) = 2/8 x 1/7

= 1/28

P(B,R) = 5/8 x 2/7

= 5/28

P(B,B) = 5/8 x 4/7

= 5/14

P(B,Y) = 5/8 x 1/7

= 5/56

P(Y,R) = 1/8 x 2/7

=1/28

P(Y,B) = 1/8 x 5/7

= 5/56

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