Jackson has a bag of skittles and pours them out on a napkin. He counts
6
orange,
9
purple,
4
red,
2
green and
7
yellow. Jackson places all the skittles back into the bag and selects one skittle with out looking, puts it back and selects another. What is the probability of Jackson choosing a green skittle? What is the probability of choosing a yellow skittle? Give a reason why.
To find the probability of Jackson choosing a green skittle, we first need to find the total number of skittles in the bag.
Total number of skittles = 6 (orange) + 9 (purple) + 4 (red) + 2 (green) + 7 (yellow) = 28
Now, the probability of choosing a green skittle is equal to the number of green skittles divided by the total number of skittles.
Probability of choosing a green skittle = 2 (number of green skittles) / 28 (total number of skittles) = 2/28 = 1/14 or approximately 0.0714 or 7.14%
Similarly, the probability of choosing a yellow skittle is equal to the number of yellow skittles divided by the total number of skittles.
Probability of choosing a yellow skittle = 7 (number of yellow skittles) / 28 (total number of skittles) = 7/28 = 1/4 or 0.25 or 25%
So, the probability of Jackson choosing a green skittle is 1/14 or approximately 7.14%, and the probability of choosing a yellow skittle is 1/4 or 25%.
The reason why the probabilities are calculated this way is due to the fact that each skittle has an equal chance of being chosen, and the total probability of all outcomes must add up to 1.