Question

there are 10 boys and 12 girls in the tennis club. the coach wants to select two players to practice first. which statements are true? check all that apply. there is approximately a 27 percent likelihood that one boy and one girl will be chosen to practice first. there is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first. there is approximately a 19 percent likelihood that two boys will be chosen to practice first. there is approximately a 19 percent likelihood that two girls will be chosen to practice first. there is approximately a 29 percent likelihood that two girls will be chosen to practice first.

Explanation:

Step1: Calculate total number of players

Total players = 10 + 12 = 22

Step2: Calculate number of ways to choose 2 players

Using combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, here $n = 22$, $r=2$, so $C(22,2)=\frac{22!}{2!(22 - 2)!}=\frac{22\times21}{2\times1}=231$

Step3: Calculate number of ways to choose 1 boy and 1 girl

Number of ways to choose 1 boy out of 10 is $C(10,1)=\frac{10!}{1!(10 - 1)!}=10$, number of ways to choose 1 girl out of 12 is $C(12,1)=\frac{12!}{1!(12 - 1)!}=12$. So number of ways to choose 1 boy and 1 girl is $10\times12 = 120$. Probability of choosing 1 boy and 1 girl is $\frac{120}{231}\approx0.52$ or 52%

Step4: Calculate number of ways to choose 2 boys

$C(10,2)=\frac{10!}{2!(10 - 2)!}=\frac{10\times9}{2\times1}=45$. Probability of choosing 2 boys is $\frac{45}{231}\approx0.19$ or 19%

Step5: Calculate number of ways to choose 2 girls

$C(12,2)=\frac{12!}{2!(12 - 2)!}=\frac{12\times11}{2\times1}=66$. Probability of choosing 2 girls is $\frac{66}{231}\approx0.29$ or 29%

Answer:

There is approximately a 52 percent likelihood that one boy and one girl will be chosen to practice first.
There is approximately a 19 percent likelihood that two boys will be chosen to practice first.
There is approximately a 29 percent likelihood that two girls will be chosen to practice first.