The probability that the event management company will sign the contract with the dance studio is:
0.023874
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:
[tex]P(X=r)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]
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:
[tex]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[/tex]
