A bit flower as has 5 begonias, 6 carnations , and 7tulips. Two flowers are randomly selected without replacement. What is the probability of selecting two carnations?
There are a total of 18 flowers, so the probability of selecting any flower on the first draw is 1/18. If a carnation is selected on the first draw, there are 5 carnations left out of 17 flowers for the second draw, so the probability of selecting another carnation is 5/17. Therefore, the probability of selecting two carnations is:
(6/18) * (5/17) = 30/306 ≈ 0.098 or 9.8%
To find the probability of selecting two carnations, we need to calculate the ratio of the number of favorable outcomes (selecting two carnations) to the total number of possible outcomes.
Step 1: Calculate the total number of flowers:
Since there are 5 begonias, 6 carnations, and 7 tulips, the total number of flowers is:
Total flowers = 5 + 6 + 7 = 18
Step 2: Calculate the number of ways to select two carnations:
Since we are selecting two flowers without replacement, we can use the combination formula:
Number of ways to select two carnations = C(6, 2) = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15
Step 3: Calculate the total number of ways to select two flowers:
Since we are selecting two flowers from a total of 18 flowers, we can use the combination formula:
Total number of ways to select two flowers = C(18, 2) = 18! / (2! * (18 - 2)!) = 18! / (2! * 16!) = (18 * 17) / (2 * 1) = 153
Step 4: Calculate the probability:
Now we can calculate the probability of selecting two carnations:
Probability = Number of ways to select two carnations / Total number of ways to select two flowers
Probability = 15 / 153 ≈ 0.098 (rounded to three decimal places)
Therefore, the probability of randomly selecting two carnations without replacement is approximately 0.098.