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. 40/900
B. 5/30
C. 8/30
D. 40/870
Is the answer D?
Thank you
Convince me that D is the correct answer
To find the probability of drawing a green gum ball and then a yellow gum ball, you need to know the total number of gum balls and the number of green and yellow gum balls.
In this case, the total number of gum balls is the sum of the individual colors:
Total number of gum balls = 9 (red) + 5 (green) + 8 (yellow) + 8 (blue) = 30
The probability of drawing a green gum ball is given by:
P(green) = Number of green gum balls / Total number of gum balls
P(green) = 5 / 30 = 1/6
Now, after taking out a green gum ball, there are 4 remaining green gum balls. The probability of drawing a yellow gum ball is given by:
P(yellow) = Number of yellow gum balls / (Total number of gum balls - 1)
P(yellow) = 8 / (30 - 1) = 8 / 29
To find the probability of both events happening (green, then yellow), you need to multiply the individual probabilities:
P(green, then yellow) = P(green) * P(yellow)
P(green, then yellow) = (1/6) * (8/29)
To simplify the answer, we can multiply the numerators and denominators:
P(green, then yellow) = (1 * 8) / (6 * 29) = 8 / 174 = 4 / 87
Therefore, the correct answer is not D (40/870), but 4/87.