What is the probability of rolling an odd number on the first roll of a six-sided cube and rolling an even number on the second roll?(1 point)
Responses
A). 1
1
B). 1/2
Start Fraction 1 over 2 End Fraction
C). 2
2
D). 1/4
3 answers
D). 1/4
A big flower vase has 5 begonias, 6 carnations, and 7 tulips. Two flowers are randomly selected without replacement. What is the probability of selecting two carnations? Express the answer in the simplest form of fraction.(1 point)
To find the probability of selecting two carnations, we first need to calculate the total number of ways to choose 2 flowers out of the total number of flowers in the vase:
Total ways to choose 2 flowers = (5 + 6 + 7) choose 2
Total ways to choose 2 flowers = (18 choose 2)
Total ways to choose 2 flowers = (18! / (2! * (18-2)!)
Total ways to choose 2 flowers = (18 * 17) / (2 * 1)
Total ways to choose 2 flowers = 153
Next, we need to determine the number of ways to select 2 carnations out of the 6 carnations available:
Number of ways to select 2 carnations = 6 choose 2
Number of ways to select 2 carnations = (6 * 5) / (2 * 1)
Number of ways to select 2 carnations = 15
Now, the probability of selecting two carnations is given by the number of ways to select 2 carnations divided by the total ways to choose 2 flowers:
Probability of selecting two carnations = Number of ways to select 2 carnations / Total ways to choose 2 flowers
Probability of selecting two carnations = 15 / 153
Probability of selecting two carnations = 5 / 51
Therefore, the probability of selecting two carnations is 5/51.
Total ways to choose 2 flowers = (5 + 6 + 7) choose 2
Total ways to choose 2 flowers = (18 choose 2)
Total ways to choose 2 flowers = (18! / (2! * (18-2)!)
Total ways to choose 2 flowers = (18 * 17) / (2 * 1)
Total ways to choose 2 flowers = 153
Next, we need to determine the number of ways to select 2 carnations out of the 6 carnations available:
Number of ways to select 2 carnations = 6 choose 2
Number of ways to select 2 carnations = (6 * 5) / (2 * 1)
Number of ways to select 2 carnations = 15
Now, the probability of selecting two carnations is given by the number of ways to select 2 carnations divided by the total ways to choose 2 flowers:
Probability of selecting two carnations = Number of ways to select 2 carnations / Total ways to choose 2 flowers
Probability of selecting two carnations = 15 / 153
Probability of selecting two carnations = 5 / 51
Therefore, the probability of selecting two carnations is 5/51.