Respuesta :
Answer:
62/95, or 0.6526
Step-by-step explanation:
To solve this, we fill find the probability that both students chosen are girls. Β We will then find the complement of this, which will be that not both students are girls.
First we find the number of ways we can choose 0 boys from a group of 8. Β This is the combination
[tex]_8C_0=\frac{8!}{(8-0)!0!}=\frac{8!}{8!0!}=1[/tex]
Next we find the number of ways we can choose 2 girls from a group of 12. Β This is the combination
[tex]_{12}C_2=\frac{12!}{(12-2)!2!}=\frac{12!}{10!2!}=\frac{12(11)}{2(1)}=66[/tex]
This gives us 1*66 = 66 ways the event "both students are girls" can happen.
Next we find the total number of ways to choose 2 students out of this group. Β There are a total of 8+12 = 20 students; this is the combination
[tex]_{20}C_2=\frac{20!}{(20-2)!2!}=\frac{20!}{18!2!}=\frac{20(19)}{2(1)}=190[/tex]
This gives us the probability 66/190, which simplifies to 33/95.
We want the complement of this. Β That means we subtract this probability from 1:
1-33/95 = 62/95 = 0.6526
