Joe draws five balls from a box containing 15 red balls, 15 black balls, 15 blue

Question

Joe draws five balls from a box containing 15 red balls, 15 black balls, 15 blue balls and 15 green balls. If he gets at least 3 balls of the same color then he discards the balls that are not of that color and replaces them with balls drawn at random from the remaining balls in the box. (For example, if he draws 3 red balls, a blue one and a black one, then he discards the bnlue and the black ones and draws 2 more balls from the remaining balls in the box.)

a) What is the probability of getting 5 balls all of the same color on the first draw?

b) What is the probability of getting 4 balls, all of the same color, on the first draw, then 1 of this color on the second draw?

c) What is the probability of getting 3 balls, all of the same color, on the first draw, then 2 of this color on the second draw?

d) What is the probability that Joe ends up with 5 balls of the same color?

Explanation / Answer

Total balls in a box= (15 Red+ 15 Black+ 15 Blue + 15 green)=60

Probability that a Red ball is selected in a draw= 1/4

Probability that a Black ball is selected in a draw= 1/4

Probability that a Blue ball is selected in a draw= 1/4

Probability that a Green ball is selected in a draw= 1/4

P(On the fourth and fifth draw getting a same color balls/ Three same color balls already drawn)=

(a)

Probability (Getting 5 balls all of the same color on the first draw)

0.002199

(b)

Probability of getting 4 balls, all of the same color, on the first draw, then 1 of this color on the second draw.

0.010997

© Probability of getting 3 balls, all of the same color, on the first

draw, then 2 of this color on the second draw

0.021994

(d)

Probability (Joe ends up with 5 balls of the same color)

= (1/4)5+(1/4)5 +(1/4)5 +(1/4)5

=4x(1/4)5

=0.003906

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