Question

In a class of 125 students, 27 are computer science majors, 46 are mechanical engineering majors, 11 are civil engineers and the rest are general engineering majors. Assume students only have one major.

Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?

Answer 1

We have given total students n = 125

Out of 125 students 46 are mechanical engineering students.

We are choosing 6 students randomly.

We have asked to find the probability none are mechanical engineering majors.

Therefore P(none are mechanical engineering majors) = 1 - P(All are mechanical engineering majors)

P(All are mechanical engineering majors) = ⁴⁶C₆ / ¹²⁵C₆ = 9366819 / 4690625500

= 0.001996923

P(none are mechanical engineering majors) = 1 - P(All are mechanical engineering majors)

= 1 - 0.001996923

= 0.998003077

Hence the probability that none are mechanical engineering majors is 0.99800 (Rounded to 4 decimal places)

Hope this will help you. Thank you :)