the science club has five female and five male students. the club will randomly select two people to compete…

the science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition. what is the probability that both people chosen are females?\no $\frac{1}{90}$\no $\frac{1}{5}$\no $\frac{2}{9}$\no $\frac{1}{4}$

the science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition. what is the probability that both people chosen are females?\no $\frac{1}{90}$\no $\frac{1}{5}$\no $\frac{2}{9}$\no $\frac{1}{4}$

Answer

Answer:

$\frac{2}{9}$

Explanation:

Step1: Calculate total number of students

$5 + 5=10$

Step2: Calculate number of ways to choose 2 students out of 10

$C(10,2)=\frac{10!}{2!(10 - 2)!}=\frac{10\times9}{2\times1}=45$

Step3: Calculate number of ways to choose 2 female students out of 5

$C(5,2)=\frac{5!}{2!(5 - 2)!}=\frac{5\times4}{2\times1}=10$

Step4: Calculate the probability

$P=\frac{C(5,2)}{C(10,2)}=\frac{10}{45}=\frac{2}{9}$