Respuesta :
Answer:
There is a 3.95% probability that none are mechanical engineering majors.
Step-by-step explanation:
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
There are 125 students.
51 of them are mechanical engineering majors and 125-51 = 74 are not mechanical engineering majors.
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?
The total number of students is 125. So total number of 6 student groups is
[tex]C_{125,6} = \frac{125!}{6!119!}[/tex]
The total number of non mechanical engineering students is 74. So the total number of 6 non mechanical engineering students is.
[tex]C_{74,6} = \frac{74!}{6!68!}[/tex]
The probability is:
[tex]\frac{C_{74,6}}{C_{125,6}} = 74/125 * 73/124 * 72/123 * 71/122 * 70/121 * 69/120 = 0.0395[/tex]
The 68/119 ends up simplified in this exercise, this is your mistake.
There is a 3.95% probability that none are mechanical engineering majors.
