Given Information:
Probability of success = 30%
Sample size = n = 3
Variable of interest = x = 2
Required Information:
Probability of exactly 2 graduates = ?
Answer:
Probability of exactly 2 graduates = P(2; 3, 0.30) = 0.189
Step-by-step explanation:
The given problem can be modeled as a binomial experiment since a random selected student can either b graduate or not therefore, there are only 2 outcomes. Each trial is independent and the probability of success is not changing from trial to trial. The number of trials in also fixed.
We know that a binomial distribution is given by
P(x; n, p) = nCx pˣ (1 - p)ⁿ⁻ˣ
Where p is the probability of success and 1 - p is the probability of failure, n is number of independent trials and x is the variable of interest.
For the given problem, we know that x = 2, n = 3 and p = 0.30
P(2; 3, 0.30) = 3C2*0.30²*(1 - 0.30)³⁻²
P(2; 3, 0.30) = 3*0.30²*(0.70)¹
P(2; 3, 0.30) = 0.189
