A math teacher randomly selects one student in a class to write a probability question on a chalkboard. The teacher then randomly selects a different student to answer the probability question. There are 18 boys in the class, and the ratio of boys to girls is 3:5. Find the probability that the teacher selects a girl first and a girl second. Write your answer as a decimal rounded to the nearest thousandth.

The probability to the nearest thousandth is 0.386

Step-by-step explanation:

Firstly, we will need to know the number of girls and the total number of students in the class.

We have the ratio as 3:5 for boys and girls with the number of boys being 18

What we have is thus;

3:5 = 18:g

3/5 = 18/g

3g = 90

g = 90/3

g = 30 girls

Thus, we have 18 boys and 30 girls with a total of 48 students.

The probability that the teacher selects a girl to write the question on the board is 30/48 = 5/8

Now, we intend selecting another girl to answer the question. This is like a probability without replacement. So this means that the number of girls we have now is 29 and the number of students we are selecting from is 47 students

Thus, the probability of selecting a girl to answer the question becomes 29/47

The joint probability is thus; 29/47 * 5/8 = 145/376 = 0.3856

To the nearest thousandth, we have 0.386