There are 9 red gum balls, 5 green gum balls, 8 yellow gum balls, and 8 blue gum balls in a machine. Find P(green, then yellow).
A. start fraction 40 over 900 end fraction
B. The term shows 5 over 30.
C. The term shows 8 over 30.
D. start fraction 40 over 870 end fraction
There are a total of 30 gum balls in the machine.
The probability of getting a green gum ball on the first draw is 5/30.
After one green gum ball has been drawn, there are 29 gum balls left in the machine, including 8 yellow gum balls. So the probability of drawing a yellow gum ball after drawing a green gum ball is 8/29.
The probability of getting a green gum ball first and then a yellow gum ball is the product of these two probabilities: 5/30 * 8/29 = 40/870.
So the answer is option D, start fraction 40 over 870 end fraction.
To find the probability of drawing a green gum ball, followed by a yellow gum ball, we need to determine the total number of gum balls and the number of green gum balls and yellow gum balls.
First, let's calculate the total number of gum balls in the machine:
Total gum balls = number of red gum balls + number of green gum balls + number of yellow gum balls + number of blue gum balls
Total gum balls = 9 + 5 + 8 + 8 = 30
Next, we need to calculate the probability of drawing a green gum ball first.
Probability of drawing a green gum ball = number of green gum balls / total number of gum balls
Probability of drawing a green gum ball = 5 / 30 = 1/6
Now, let's calculate the probability of drawing a yellow gum ball after drawing a green gum ball.
Since we don't replace the gum ball after drawing, the total number of gum balls decreases by 1. Therefore, the total number of gum balls for this step is 29.
Probability of drawing a yellow gum ball after drawing a green gum ball = number of yellow gum balls / total number of gum balls
Probability of drawing a yellow gum ball after drawing a green gum ball = 8 / 29
Now, let's multiply the probabilities together to find the probability of drawing a green gum ball, then drawing a yellow gum ball.
P(green, then yellow) = (1/6) * (8/29)
Simplifying the expression:
P(green, then yellow) = 8 / (6 * 29)
P(green, then yellow) = 8 / 174
Therefore, the correct answer is:
D. start fraction 40 over 870 end fraction
To find the probability of drawing a green gum ball and then a yellow gum ball, we need to find the probability of each individual event occurring and then multiply them together.
The probability of drawing a green gum ball can be calculated by dividing the number of green gum balls (5) by the total number of gum balls in the machine (9 + 5 + 8 + 8 = 30).
So, the probability of drawing a green gum ball is 5/30.
After drawing a green gum ball, there will be 29 gum balls left in the machine (since one green gum ball has already been drawn). The probability of drawing a yellow gum ball can be calculated by dividing the number of yellow gum balls (8) by the remaining number of gum balls in the machine (29).
So, the probability of drawing a yellow gum ball after a green gum ball has been drawn is 8/29.
To find the probability of both events occurring, we multiply their probabilities together:
P(green, then yellow) = (5/30) * (8/29)
Simplifying the expression, we get:
P(green, then yellow) = 40/870
Therefore, the correct answer is option D: start fraction 40 over 870 end fraction.