Three (3) scholars will be picked randomly from a set of qualifiers consisting of 2 girls and 4 boys. What is the probability that 2 boys and a girl will be chosen?
There are a total of 6 people from which 3 will be picked randomly, so there are 6C3 = 20 possible combinations of scholars that can be chosen.
To calculate the probability of selecting 2 boys and a girl, we need to find the number of ways that this can occur. There are 4C2 ways to choose 2 boys from the 4 available, and 2C1 ways to choose 1 girl from the 2 available. Thus, the number of possible combinations of scholars that consist of 2 boys and 1 girl is:
4C2 * 2C1 = 6 * 2 = 12
Therefore, the probability of selecting 2 boys and 1 girl is:
12/20 = 0.6 or 60%
To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the total number of possible outcomes. Since 3 scholars will be chosen randomly from a set of 2 girls and 4 boys, the total number of possible outcomes can be calculated using combinations.
The total number of possible outcomes can be calculated as:
Total number of possible outcomes = C(6, 3) = 6! / (3!(6-3)!) = 20
Now, let's determine the number of favorable outcomes, i.e., the number of ways to select 2 boys and 1 girl.
The number of favorable outcomes can be calculated as:
Number of favorable outcomes = C(4, 2) * C(2, 1) = (4! / (2!(4-2)!) * (2! / (1!(2-1)!) = 6 * 2 = 12
Finally, we can calculate the probability that 2 boys and 1 girl will be chosen as:
Probability = Favorable outcomes / Total outcomes = 12 / 20 = 0.6
Therefore, the probability that 2 boys and 1 girl will be chosen is 0.6 or 60%.