An art class consists of 8 boys and 10 girls. The teacher randomly chooses 3 students to present their work. Find the probability that all 3 of the students chosen are girls.
To find the probability that all 3 of the students chosen are girls, we need to know the total number of ways to choose 3 students from the entire class and the number of ways to choose 3 girls from the class.
First, let's calculate the total number of ways to choose 3 students from the class of 18 (8 boys and 10 girls).
This can be done using the concept of combinations - specifically, the formula for calculating combinations is nCr = n! / (r!(n-r)!), where n is the total number of objects, and r is the number of objects being chosen.
In this case, n = 18 (the total number of students in the class) and r = 3 (the number of students being chosen).
So the total number of ways to choose 3 students from the class is:
18C3 = 18! / (3!(18-3)!) = 18! / (3!15!) = (18 * 17 * 16) / (3 * 2 * 1) = 816.
Now, let's calculate the number of ways to choose 3 girls from the class of 10.
We can use the same formula, but this time, n = 10 (the total number of girls in the class) and r = 3 (the number of girls being chosen).
So the number of ways to choose 3 girls is:
10C3 = 10! / (3!(10-3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.
Finally, the probability that all 3 chosen students are girls is equal to the number of ways to choose 3 girls divided by the total number of ways to choose 3 students:
Probability = (number of ways to choose 3 girls) / (total number of ways to choose 3 students)
Probability = 120 / 816
Probability = 0.1471 (rounded to four decimal places)
Therefore, the probability that all 3 of the students chosen are girls is approximately 0.1471.