In a classroom of 20 students. 14 of them have brown eyes. If a teacher picks 2 students at random to pass out supplies, what is the probability she chooses 2 students without brown eyes?
6 of the 20 have other colors
6/20 for the first one
now you have 5 out of 19 left
so
6/20 * 5/19
consider this like selection without replacement. So, with 6 students without brown eyes, the probability of drawing two of them is
6/20 * 5/19
aa
To find the probability of the teacher choosing 2 students without brown eyes, we need to calculate the number of favorable outcomes (choosing 2 students without brown eyes) and divide it by the total number of possible outcomes (choosing any 2 students).
Let's start by calculating the number of favorable outcomes. We know that there are 14 students with brown eyes in a classroom of 20 students. So, the number of students without brown eyes is 20 - 14 = 6.
To choose 2 students without brown eyes, we need to select 2 out of the 6 students without brown eyes. The number of ways to choose 2 students out of 6 can be calculated using combinations. The formula for combinations is given by C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items you want to choose.
So, the number of ways to choose 2 students without brown eyes from a group of 6 students is C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4 * 3 * 2 * 1) / ((2 * 1) * (4 * 3 * 2 * 1)) = (6 * 5) / (2 * 1) = 15.
Now, let's calculate the total number of possible outcomes, which is the number of ways to choose any 2 students from a group of 20 students. This can also be calculated using combinations. So, the number of ways to choose 2 students from a group of 20 students is C(20, 2) = 20! / (2! * (20-2)!) = 20! / (2! * 18!) = (20 * 19) / (2 * 1) = 190.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 15 / 190 = 0.079 or 7.9%.
Therefore, the probability that the teacher chooses 2 students without brown eyes is approximately 0.079 or 7.9%.