Suppose a box has eight differently colored tennis balls in it. The colors are green, blue, red, purple, orange, black, and white.
if I will randomly pick out three balls (without replacement), then what is the probability that the balls chosen will be green, yellow, and red (in that order)? Show work. Write your answers as a fraction and adecimal rounded with four nonzero digits
For the first pick, we need a green out of 8 balls. For the second pick, we need a yellow out of 7 balls. For the last pick, we need a red out of 6 balls.
By the multiplication rule, the probability is
P(G,Y,R)=(1/8)(1/7)(1/6)
I'll leave it to you to do the arithmetic.
To determine the probability of selecting three balls in a specific order, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When selecting three balls without replacement, the first ball can be any of the eight available colors. After picking the first ball, the second ball can be any of the remaining seven colors, and the third ball can be any of the remaining six colors. Therefore, the total number of outcomes is 8 x 7 x 6 = 336.
Number of favorable outcomes:
To have a favorable outcome of green, yellow, and red in that order, we must consider that there are no yellow balls in the box. Therefore, it is impossible to select a yellow ball, and there are zero favorable outcomes.
Probability:
The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, since there are no favorable outcomes, the probability is 0.
As a fraction: 0/336 = 0
As a decimal rounded to four nonzero digits: 0.0000.