Two flower seeds are randomly selected from a package that contains five seeds for red flowers and three seeds for white flowers.
a.) What is the probability that both seeds will result in red flowers?
b.) What is the probability that one of each color is selected?
c.) What is the probability that both seeds are for white flowers?
a) first one : prob = (5/8)(4/7) = 5/14
b) could be RW or WR,
so (5/8)(3/7) + (3/8)(5/7) = 2(15/56) = 15/28
c) let me know what you get for this one.
a.) What is the probability that both seeds will result in red flowers?
Well, since there are five seeds for red flowers and eight total seeds, the probability of the first seed being red is 5/8. Then, since there are four red seeds left and seven total seeds, the probability of the second seed being red is 4/7. To find the probability of both events occurring, we multiply the individual probabilities together: (5/8) * (4/7) = 20/56. Simplifying, we get a final probability of 5/14.
b.) What is the probability that one of each color is selected?
To find this probability, we need to calculate two scenarios: one where the red seed is selected first and the white seed second, and another where the white seed is selected first and the red seed second. Let's break it down!
Scenario 1: The probability of the first seed being red is 5/8. Then, since there are three white seeds left and seven total seeds, the probability of the second seed being white is 3/7.
Scenario 2: The probability of the first seed being white is 3/8. Then, since there are five red seeds left and seven total seeds, the probability of the second seed being red is 5/7.
Now, since we have two mutually exclusive scenarios (we can't have both a red seed first and a white seed first), we can add the two probabilities together: (5/8) * (3/7) + (3/8) * (5/7) = 15/56 + 15/56 = 30/56. Simplifying, we get a final probability of 15/28.
c.) What is the probability that both seeds are for white flowers?
Similarly to part (a), the probability of the first seed being white is 3/8. Then, since there are two white seeds left and seven total seeds, the probability of the second seed being white is 2/7. Multiplying these probabilities together, we get (3/8) * (2/7) = 6/56. Simplifying, we get a final probability of 3/28.
To find the probabilities, we need to know the total number of possible outcomes and the number of favorable outcomes for each event.
a.) Probability that both seeds will result in red flowers:
Total number of possible outcomes = Total number of seeds = 5 (red flower seeds) + 3 (white flower seeds) = 8
Number of favorable outcomes = Number of ways to choose 2 red flower seeds from the 5 available = Combination(5, 2) = 10
Probability = Number of favorable outcomes / Total number of possible outcomes = 10 / 8 = 5 / 4 = 1.25
However, probability can only be between 0 and 1, so the probability is 1 since having more than one seed selected is not possible.
b.) Probability that one of each color is selected:
Total number of possible outcomes = Total number of seeds = 5 (red flower seeds) + 3 (white flower seeds) = 8
Number of favorable outcomes = Number of ways to choose 1 red flower seed from the 5 available * Number of ways to choose 1 white flower seed from the 3 available = Combination(5, 1) * Combination(3, 1) = 5 * 3 = 15
Probability = Number of favorable outcomes / Total number of possible outcomes = 15 / 8 = 1.875
However, probability can only be between 0 and 1, so the probability is 1 since having more than one seed selected is not possible.
c.) Probability that both seeds are for white flowers:
Total number of possible outcomes = Total number of seeds = 5 (red flower seeds) + 3 (white flower seeds) = 8
Number of favorable outcomes = Number of ways to choose 2 white flower seeds from the 3 available = Combination(3, 2) = 3
Probability = Number of favorable outcomes / Total number of possible outcomes = 3 / 8 = 0.375
To find the probabilities, we need to use the concept of combinations. The formula to calculate the probabilities is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Let's calculate each probability step by step:
a.) Probability of both seeds resulting in red flowers:
Step 1: Determine the total number of possible outcomes.
Since there are 5 seeds for red flowers and 3 seeds for white flowers, the total number of seeds in the package is 5 + 3 = 8 seeds.
Step 2: Determine the number of favorable outcomes.
To select 2 red flower seeds, we need to choose 2 seeds out of the 5 red flower seeds. We can use the combination formula here.
Number of combinations = C(5, 2) = 5! / (2! * (5 - 2)!) = 10
Step 3: Calculate the probability.
Probability of both seeds being red = Number of favorable outcomes / Total number of possible outcomes = 10 / 8 = 5 / 4 = 1.25
b.) Probability of one red and one white seed being selected:
Step 1: Determine the total number of possible outcomes.
The total number of seeds remains the same, so the total number of possible outcomes is still 8 seeds.
Step 2: Determine the number of favorable outcomes.
To have one red and one white seed, we need to choose 1 red seed out of the 5 available and 1 white seed out of the 3 available. Again, we can use the combination formula.
Number of combinations = C(5, 1) * C(3, 1) = (5! / (1! * (5 - 1)!)) * (3! / (1! * (3 - 1)!)) = 5 * 3 = 15
Step 3: Calculate the probability.
Probability of selecting one seed each = Number of favorable outcomes / Total number of possible outcomes = 15 / 8 = 15 / 8 = 1.875
c.) Probability of both seeds resulting in white flowers:
Step 1: Determine the total number of possible outcomes (same as in the previous steps) = 8 seeds.
Step 2: Determine the number of favorable outcomes.
To select 2 white flower seeds, we need to choose 2 seeds out of the 3 white flower seeds.
Number of combinations = C(3, 2) = 3! / (2! * (3 - 2)!) = 3
Step 3: Calculate the probability.
Probability of both seeds being white = Number of favorable outcomes / Total number of possible outcomes = 3 / 8 = 0.375
So, to summarize:
a.) The probability that both seeds will result in red flowers is 1.25 or 5/4.
b.) The probability that one of each color is selected is 1.875 or 15/8.
c.) The probability that both seeds are for white flowers is 0.375 or 3/8.