Can someone help me answer this question, so I would know what to do for a question like this next time?
Thank you!
A box contains 10 red chips, 20 blue chips, and 30 green chips. If 5 chips are drawn from the box, find the probability of drawing
a.) exactly 4 green
b.) at least 2 red
c.) at most 2 blue
Sure, I can help you with that! To find the probability of an event, we need to know the total number of possible outcomes and the number of favorable outcomes.
a.) To find the probability of drawing exactly 4 green chips, we need to calculate the probability of drawing 4 green chips and 1 chip that is not green. First, we calculate the total number of possible outcomes, which is the number of ways to draw any 5 chips from the box. This can be calculated using combinations.
The total number of possible outcomes = C(60, 5) = 60! / (5! * 55!) = 6,724,530
Next, we calculate the number of favorable outcomes, which is the number of ways to draw exactly 4 green chips and 1 chip that is not green. The number of ways to choose 4 green chips from the 30 green chips is C(30, 4) = 27,405. Then, we choose 1 chip that is not green from the remaining 30 chips, which is C(30, 1) = 30.
The number of favorable outcomes = C(30, 4) * C(30, 1) = 27,405 * 30 = 822,150
Now we can find the probability by dividing the favorable outcomes by the total possible outcomes:
Probability of drawing exactly 4 green = favorable outcomes / total possible outcomes = 822,150 / 6,724,530 ≈ 0.122
So the probability of drawing exactly 4 green chips is approximately 0.122.
b.) To find the probability of drawing at least 2 red chips, we need to calculate the probability of drawing 2, 3, 4, or 5 red chips. We can add up the individual probabilities for each case.
Probability of drawing 2 red = C(10, 2) * C(50, 3) / C(60, 5)
Probability of drawing 3 red = C(10, 3) * C(50, 2) / C(60, 5)
Probability of drawing 4 red = C(10, 4) * C(50, 1) / C(60, 5)
Probability of drawing 5 red = C(10, 5) * C(50, 0) / C(60, 5)
Now, for each case, we calculate the probability and add them together to get the probability of drawing at least 2 red chips.
c.) To find the probability of drawing at most 2 blue chips, we need to calculate the probability of drawing 0, 1, or 2 blue chips. We do the same as in part b) by calculating the individual probabilities for each case and adding them together.
I hope this explanation helps you understand how to approach these types of probability questions!