A local company has been in trouble recently over hiring male applicants rather than female. Recently 3 employees hired were all male even though the six applicants for the 3 positions included 3 females. The company claims that they have shaped up. From a pool of the 3 females and 2 men the company filled 2 positions with 2 females. What is the probability of that event?

To calculate the probability of the event, we need to determine the number of favorable outcomes (2 females hired) and the total number of possible outcomes (5 applicants).

Step 1: Calculate the number of ways to choose 2 females out of 3.
This can be done using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of applicants and r is the number of females to be chosen.
In this case, n = 3 and r = 2.
So, C(3, 2) = 3! / (2!(3-2)!) = 3! / (2!1!) = 3.

Step 2: Calculate the number of ways to choose 2 females and 0 males from the total pool of 5 applicants.
Again, this can be done using the combination formula.
The total number of applicants is 5, and we need to choose 2 females and 0 males.
C(5, 2) = 5! / (2!(5-2)!) = 5! / (2!3!) = 5 * 4 / (2 * 1) = 10.

Step 3: 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)
Probability = 3 / 10 = 0.3 = 30%.

Therefore, the probability of the company hiring 2 females from a pool of 3 females and 2 males is 30%.