Answer:
The probability that the teacher selects a girl first and a girl second is 0.352
Step-by-step explanation:
Number of boys in class = 12
let number of boys in class = 2x
number of girls in class = 3x
According to the question,
2x = 12
x = 6
So, number of girls = 3x = 3 × 6 = 18
Total number of students = 18 + 12 = 30
[tex]Probabiltiy=\frac{Number\:of\:favorable\:outcome}{Number\:of\:Total\:outcome}[/tex]
Probability of selecting a girl first and second girl = [tex]\frac{18}{30}\times\frac{17}{29}[/tex]
[tex]=\frac{51}{145}=0.352\:(nearest\:thousandth)[/tex]
Therefore, The probability that the teacher selects a girl first and a girl second is 0.352
The probability that the teacher selects a girl first and a girl second is 0.352 when there are 12 boys in the class, and the ratio of boys to girls is 2:3
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have:
Number of boys in the class = 12
The ratio of boys to girls is 2:3
Let's suppose the number of boys is 2x and
The number of girls is 3x
So 2x = 12 (given)
x = 6 (divide by 2 on both sides)
Now the number of girls = 3x ⇒ 3×6 ⇒ 18 girls
Number of total students in the class = 12 + 18 ⇒ = 30
Now the probability that the teacher selects a girl first and a girl second:
[tex]\rm = \frac{18}{30} \times\frac{17}{30}[/tex]
[tex]=\frac{306}{870}[/tex] or
[tex]=\frac{51}{145}[/tex] (divide by 6 on numerator and denominator)
= 0.3517 ≈ 0.352
Thus, the probability that the teacher selects a girl first and a girl second is 0.352.
Learn more about the probability here:
brainly.com/question/11234923
