An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color (b) of all different colors

Repeat the experiment under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next selection. This is known as sampling with replacement. What is the probability that each of the balls will be:

(c) of the same color

(d) of all different colors

a) 0.08875

b) 0.247678

c) 0.03499

d) 0.12436

Step-by-step explanation:

Number of red balls = 5

number of blue balls = 6

number of green balls = 8

Total number of balls = 5 + 6 + 8 = 19

with three balls selected at random, by using combination method;

nCr = n! / (n-r) ! r!

a) P (of the same color) = 5C3 + 6C3 + 8C3 / 19C3

= 86/969 = 0.08875

b) P (of different color) = 5C1 X 6C1 X 8C1 / 19C3

= 240/969 = 0.247678

When the balls are replaced i. e probability with replacement

c) P (of the same color) = 5/19 x 6/19 x 8/19

= 0.03499

d) P (of different color) = 5/19 x 5/19 x 5/19 + 6/19 x 6/19 x 6/19 + 8/19 x 8/19 x 8/19

= 0.12436