a big flower vase has 5 begonias, 6 carnations, and 7 tulips. two flowers are randomly selected without…

Explanation:

Step1: Calculate total number of flowers

The total number of flowers is $5 + 6+7=18$.

Step2: Calculate probability of first - carnation selection

The probability of selecting a carnation on the first draw is $\frac{6}{18}$ since there are 6 carnations out of 18 total flowers.

Step3: Calculate probability of second - carnation selection

Since we are drawing without replacement, after the first carnation is drawn, there are 5 carnations left and 17 total flowers left. So the probability of selecting a carnation on the second draw given that a carnation was selected on the first draw is $\frac{5}{17}$.

Step4: Calculate the probability of both events

By the multiplication rule for independent events (in the non - replacement case, sequential events), the probability of selecting two carnations is $\frac{6}{18}\times\frac{5}{17}=\frac{30}{306}=\frac{5}{51}$.

Answer:

$\frac{5}{51}$