Question

Select the correct answer.
A dance studio teaches students a contemporary dance form. It is observed that the probability of students from this studio becoming dance teachers is 0.69. An event management company wants to use this studio for a show. They decide to observe it for a year before making the deal. They enroll 120 students of their own in this studio and decide that once 75 of them get jobs as dance teachers, they will sign the contract with them. What is the probability that the event management company will sign the contract with the dance studio?
A.
0.076
B.
0.053
C.
0.024
D.
0.924
E.
0.947

Answer 1

The scenario can be categorized as a binomial probability distribution, P(x=k)=B(n, p, k), as there is a defined number of trials and two outcomes, a probability of success and failure.

Let the probability of success, p, represent the probability of becoming a dance teacher. p=0.69
Let the trials, n, be the students in the studio to be enrolled, 120.
Let k be 75, or the necessary successes to allow the contract signature.

Calculate P(k=75) for B(120, 0.69, 75)

P(k=75) = \[P(k=75)= B(120, 0.69, 75)=\left(\begin{matrix}120 \\ 75\end{matrix}\right)0.69^{75}(1-0.69)^{120-75} = 0.02387 ≈ 0.024\]

Answer 2

So yeah C is your answer