Question

. A box contains four red, three yellow, and seven green balls. Three balls are randomly selected from the box without replacement. (a) What is the probability that all three balls are the same colo

Answer 1

10/91

Explanation:

Number of Red balls = 4

Number of Yellow balls = 3

Number of green balls=7

Total=4+3+7=14

If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).

Therefore:

The probability that all three balls are the same color (note that the selections are without replacement)

=P(RRR)+P(GGG)+P(YYY)

`=((4)/(14) * (3)/(13) * (2)/(12))+((3)/(14) * (2)/(13) * (1)/(12))+((7)/(14) * (6)/(13) * (5)/(12))\\\\=(1)/(91) + (1)/(364)+ (5)/(52)\\\\=(10)/(91)`

The probability that all three balls are the same color is 10/91.