Final answer:
To find the probability of randomly withdrawing 8 jellybeans with specific numbers of red, orange, and green ones, we need to calculate the total number of possible outcomes and the number of favorable outcomes. Then, divide the number of favorable outcomes by the total number of possible outcomes to get the probability. In this case, the probability is 4.
Step-by-step explanation:
To find the probability of reaching into the bag and randomly withdrawing 8 jellybeans such that there are 3 red ones, 2 orange ones, and 3 green ones, we need to determine the total number of possible outcomes and the number of favorable outcomes.
There are 14 jellybeans in total: 4 red, 5 orange, and 5 green. The total number of possible outcomes is given by the equation:
Total number of possible outcomes = (number of red jellybeans) * (number of orange jellybeans) * (number of green jellybeans)
Total number of possible outcomes = 4 * 5 * 5 = 100
The number of favorable outcomes is the number of ways to choose 3 red jellybeans out of 4, 2 orange jellybeans out of 5, and 3 green jellybeans out of 5:
Number of favorable outcomes = (number of ways to choose 3 red jellybeans out of 4) * (number of ways to choose 2 orange jellybeans out of 5) * (number of ways to choose 3 green jellybeans out of 5)
Number of favorable outcomes = C(4, 3) * C(5, 2) * C(5, 3)
Number of favorable outcomes = 4 * 10 * 10 = 400
The probability of drawing 8 jellybeans with 3 red, 2 orange, and 3 green is given by the equation:
Probability = (number of favorable outcomes) / (total number of possible outcomes)
Probability = 400 / 100 = 4