Out of 90 applicants for a job, 60 people get selected after the interview. If five applicants are selected at random,calculate the probability that 2 will get selected.
To calculate the probability that 2 out of 5 applicants will get selected, we need to use the concept of combinations.
First, let's determine the total number of ways to choose 5 applicants out of the 90 applicants:
This can be calculated using the combination formula, given by:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of applicants (90 in this case) and r is the number of applicants to be selected (5 in this case).
Using this formula, we have:
C(90, 5) = 90! / (5!(90 - 5)!)
= 90! / (5!85!)
Next, let's determine the number of ways to choose 2 applicants out of the selected 60 applicants:
This can be calculated using the same combination formula, but with n as 60 and r as 2:
C(60, 2) = 60! / (2!(60 - 2)!)
= 60! / (2!58!)
Now, we can calculate the probability of selecting exactly 2 applicants out of the 5 randomly selected applicants:
Probability = Number of favorable outcomes / Total number of possible outcomes
The number of favorable outcomes is the number of ways to choose 2 applicants out of the selected 60 applicants.
The total number of possible outcomes is the number of ways to choose 5 applicants out of the 90 applicants.
So, the probability will be:
Probability = C(60, 2) / C(90, 5)
You can plug these values into a calculator or use software like Excel to calculate the probability.