Two flower seeds are randomly selected from a package tha tcontains 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?

What is the probability that washing dishes tonight will take me between 13 and 16 minutes?

Give your answer accurate to two decimal places

0.54

a.) To find the probability that both seeds will result in red flowers, we need to calculate the probability of selecting a red flower seed twice.

The total number of seeds in the package is 5 for red flowers + 3 for white flowers = 8 seeds.

The probability of selecting a red flower seed on the first draw is 5 red seeds / 8 total seeds.

After the first draw, there are 4 red seeds left and 7 total seeds remaining.

So, the probability of selecting a red flower seed on the second draw is 4 red seeds / 7 total seeds.

To find the probability of both events happening, we multiply the probabilities: (5/8) * (4/7) = 20/56 = 5/14.

Therefore, the probability that both seeds will result in red flowers is 5/14.

b.) To find the probability that one of each color is selected, we need to calculate the probability of one red seed and one white seed being chosen.

The probability of selecting a red flower seed on the first draw is 5 red seeds / 8 total seeds.

After the first draw, there are 4 red seeds left and 7 total seeds remaining.

The probability of selecting a white flower seed on the second draw is 3 white seeds / 7 total seeds.

Since the order of selection does not matter, we need to consider both possibilities: red first, then white, or white first, then red.

So, the probability of selecting one of each color is (5/8) * (3/7) + (3/8) * (5/7) = 15/56 + 15/56 = 30/56 = 15/28.

Therefore, the probability that one of each color is selected is 15/28.

c.) To find the probability that both seeds are for white flowers, we need to calculate the probability of selecting a white flower seed twice.

The probability of selecting a white flower seed on the first draw is 3 white seeds / 8 total seeds.

After the first draw, there are 2 white seeds left and 7 total seeds remaining.

So, the probability of selecting a white flower seed on the second draw is 2 white seeds / 7 total seeds.

To find the probability of both events happening, we multiply the probabilities: (3/8) * (2/7) = 6/56 = 3/28.

Therefore, the probability that both seeds are for white flowers is 3/28.

To find the probabilities, we will be using the concept of probability and combinations.

a) What is the probability that both seeds will result in red flowers?

To find the probability, we need to determine the total number of outcomes and the number of favorable outcomes.

Total outcomes = Total number of ways to select any 2 seeds from the package = combination(8, 2) = 8! / (2!(8-2)!) = 28

Number of favorable outcomes = Number of ways to select 2 red seeds from the 5 available = combination(5, 2) = 5! / (2!(5-2)!) = 10

Therefore, the probability that both seeds will result in red flowers is 10/28 or simplified as 5/14.

b) What is the probability that one of each color is selected?

To find this probability, we need to determine the total number of outcomes and the number of favorable outcomes.

Total outcomes = Total number of ways to select any 2 seeds from the package = combination(8, 2) = 28 (as calculated earlier)

Number of favorable outcomes = Number of ways to select 1 red seed and 1 white seed from the package.
For red seed: combination(5, 1) = 5
For white seed: combination(3, 1) = 3

Total favorable outcomes = Number of ways to select 1 red seed and 1 white seed = 5 * 3 = 15

Therefore, the probability that one of each color is selected is 15/28.

c) What is the probability that both seeds are for white flowers?

To find this probability, we need to determine the total number of outcomes and the number of favorable outcomes.

Total outcomes = Total number of ways to select any 2 seeds from the package = combination(8, 2) = 28 (as calculated earlier)

Number of favorable outcomes = Number of ways to select 2 white seeds from the 3 available = combination(3, 2) = 3

Therefore, the probability that both seeds are for white flowers is 3/28.

Please note that these calculations assume that the selection is made without replacement, meaning once a seed is selected, it is not put back in the package before selecting the second seed.