Question
Probability Unit Test
13 of 1513 of 15 Items
QuestionA 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.
Answers
GPT 3.5
To find the probability of selecting two carnations, we first find the total number of ways to choose 2 flowers out of 18 (5 begonias + 6 carnations + 7 tulips). This can be calculated using combinations:
Total number of ways to choose 2 flowers out of 18 = 18C2 = 153
Next, we find the number of ways to choose 2 carnations out of 6:
Number of ways to choose 2 carnations out of 6 = 6C2 = 15
Therefore, the probability of selecting two carnations is:
Probability = Number of ways to choose 2 carnations / Total number of ways to choose 2 flowers
Probability = 15 / 153
The probability of selecting two carnations is 15/153, which simplifies to 5/51.
Total number of ways to choose 2 flowers out of 18 = 18C2 = 153
Next, we find the number of ways to choose 2 carnations out of 6:
Number of ways to choose 2 carnations out of 6 = 6C2 = 15
Therefore, the probability of selecting two carnations is:
Probability = Number of ways to choose 2 carnations / Total number of ways to choose 2 flowers
Probability = 15 / 153
The probability of selecting two carnations is 15/153, which simplifies to 5/51.