Question

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?

Answer 1

approximately 0.0239 > 0.024

Answer 2

The probability that the event management company will sign the contract with the dance studio is:

0.023874

Explanation:

We need to use the binomial in order to find the probability.

We know that the probability of r successes in n experiments is given by:

`P(X=r)=n_C_r\cdot p^r\cdot (1-p)^(n-r)`

where p is the probability of success.

Based on the information we have:

n=120 and r=75

( since, They enroll 120 students of their own in this studio and decide that once 75 of them get jobs as dance teachers)

and p=0.69

( It is observed that the probability of students from this studio becoming dance teachers is 0.69 )

Hence, we get:

`P(X=75)={120}_C_(75)\cdot (0.69)^(75)\cdot (1-0.69)^(120-75)\\\\\\P(X=75)={120}_C_(75)\cdot (0.69)^(75)\cdot (0.31)^(45)\\\\\\P(X=75)=0.023874`