Question

after a health class lesson on antioxidants found in food, molly ordered a variety of seeds to start a tomato garden. in total, mollys order included 18 seeds, 8 of which were roma tomato seeds and 5 of which are cherry tomato seeds. if molly randomly selected 4 of the seeds to plant in a certain order in the front yard, what is the probability that the first 2 seeds are roma tomato seeds and the last 2 are cherry tomato seeds? write your answer as a decimal rounded to four decimal places.

Explanation:

Step1: Calculate probability of first roma seed

The probability of choosing a roma tomato seed first is $\frac{8}{18}$ since there are 8 roma tomato seeds out of 18 total seeds.

Step2: Calculate probability of second roma seed

After choosing one roma seed, there are 7 roma seeds left out of 17 total seeds. So the probability of choosing a second roma seed is $\frac{7}{17}$.

Step3: Calculate probability of first cherry seed

After choosing 2 roma seeds, there are 5 cherry tomato seeds out of 16 total seeds. So the probability of choosing a cherry tomato seed third is $\frac{5}{16}$.

Step4: Calculate probability of second cherry seed

After choosing 3 seeds, there are 4 cherry seeds left out of 15 total seeds. So the probability of choosing a cherry tomato seed fourth is $\frac{4}{15}$.

Step5: Calculate overall probability

The overall probability is the product of the probabilities of each step. So $P=\frac{8}{18}\times\frac{7}{17}\times\frac{5}{16}\times\frac{4}{15}=\frac{8\times7\times5\times4}{18\times17\times16\times15}=\frac{1120}{73440}\approx0.0152$.

Answer:

0.0152