A bowl contains 25 red and 20 green candy canes. If two candy canes are drawn WITHOUT replacement, determine the following probabilities
To determine the probabilities in this scenario, we need to understand the concept of probability and the principles of counting.
First, let's define a few terms:
- "Without replacement" means that once a candy cane is drawn, it is not put back into the bowl before the next draw.
- "Probability" refers to the likelihood of a specific event occurring, which is expressed as a number between 0 and 1.
Now, let's calculate the probabilities step by step:
1. Probability of drawing two red candy canes:
We have 25 red candy canes out of a total of 45 (25 red + 20 green) candy canes in the bowl. When we draw the first candy cane, we have a 25/45 chance of getting a red one. After the first draw, there are 24 red candy canes left out of the remaining 44. Therefore, the probability of drawing two red candy canes is calculated as:
P(RR) = (25/45) * (24/44) = 600/1980 ≈ 0.303 (approximately)
2. Probability of drawing two green candy canes:
Similarly, we have 20 green candy canes out of a total of 45 in the bowl. The probability of drawing two green candy canes is:
P(GG) = (20/45) * (19/44) = 380/1980 ≈ 0.192 (approximately)
3. Probability of drawing one red and one green candy cane:
To calculate this probability, we need to consider two possible cases:
a) Drawing a red candy cane first, then a green one:
P(RG) = (25/45) * (20/44) = 500/1980 ≈ 0.253 (approximately)
b) Drawing a green candy cane first, then a red one:
P(GR) = (20/45) * (25/44) = 500/1980 ≈ 0.253 (approximately)
We sum the probabilities from these two cases to get the final probability:
P(RG or GR) = P(RG) + P(GR) = 500/1980 + 500/1980 = 1000/1980 ≈ 0.505 (approximately)
Note: The probabilities presented here are based on the assumption that the candy canes are equally likely to be drawn and that no additional information about preference or order is given.
I hope this explanation helps you understand how to calculate the probabilities in this scenario!