The scenario that the event management enters a contract with the dance studio is bounded by binomial probability, such that the success of 75 random students is put on a trial. The probability that they sign the contract is 0.0238.
Given that:
[tex]n = 120[/tex] -- all students that enrolled
[tex]x = 75[/tex] --- the selected students
[tex]p = 0.69[/tex] --- proportion that become dance teachers
The question is an illustration of binomial probability, and it is represented as:
[tex]Pr(x) = ^nC_x \times p^x \times (1 - p)^{n-x}[/tex]
The probability that 75 becomes dance teacher is represented as: P(75)
And it is calculated as follows:
[tex]Pr(x) = ^nC_x \times p^x \times (1 - p)^{n-x}[/tex]
[tex]P(75) = ^{120}C_{75} \times 0.69^{75} \times (1 - 0.69)^{120-75}[/tex]
[tex]P(75) = ^{120}C_{75} \times 0.69^{75} \times (1 - 0.69)^{45}[/tex]
[tex]P(75) = 2.25 \times 10^{33} \times 0.69^{75} \times 0.31^{45}[/tex]
[tex]P(75) = 0.02383090557[/tex]
[tex]P(75) = 0.0238[/tex] --- Approximate
Hence, the probability that the event management signs the contract is: 0.0238
Read more about binomial probability at:
https://brainly.com/question/14214595
