kaylee bought 7 seeds in order to plant an herb garden for her grandma. of the seeds she bought, 5 were…

kaylee bought 7 seeds in order to plant an herb garden for her grandma. of the seeds she bought, 5 were parsley seeds. if kaylee chooses to plant 4 random seeds on the east side of the garden, what is the probability that all of them are parsley seeds? write your answer as a decimal rounded to four decimal places.

kaylee bought 7 seeds in order to plant an herb garden for her grandma. of the seeds she bought, 5 were parsley seeds. if kaylee chooses to plant 4 random seeds on the east side of the garden, what is the probability that all of them are parsley seeds? write your answer as a decimal rounded to four decimal places.

Answer

Explanation:

Step1: Calculate total ways to choose 4 seeds out of 7

We use combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 7$ and $r=4$. So $C(7,4)=\frac{7!}{4!(7 - 4)!}=\frac{7!}{4!3!}=\frac{7\times6\times5}{3\times2\times1}=35$.

Step2: Calculate ways to choose 4 parsley seeds out of 5

Using combination formula with $n = 5$ and $r = 4$. So $C(5,4)=\frac{5!}{4!(5 - 4)!}=\frac{5!}{4!1!}=5$.

Step3: Calculate the probability

Probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{C(5,4)}{C(7,4)}=\frac{5}{35}=\frac{1}{7}\approx0.1429$.

Answer:

0.1429