Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

D). 1/4

Answer 2

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)

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.