SOLUTION: In a class of 140 students, 32 are computer science majors, 49 are mechanical engineering majors, 12 are civil engineers and the rest are general engineering majors. Assume student

Question 1185015: In a class of 140 students, 32 are computer science majors, 49 are mechanical engineering majors, 12 are civil engineers and the rest are general engineering majors. Assume students can only have one major.
If a student is chosen at random what is the probability they are:
Suppose five students from the class are chosen at random. What is the probability that none are mechanical engineering majors?
Please show step by step including the number in the solution. Thank you.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There are 140 students, of whom 49 are mechanical engineering majors.

The total number of ways of choosing 5 students is C(140,5); the number of ways of choosing 5 students from those that are not mechanical engineering majors is C((140-49),5) = C(91,5).

The probability of choosing 5 students of whom none are mechanical engineering majors is

= 0.11153 to 5 decimal places.

Note you would probably do the calculation using a calculator that can calculate numbers like C(140,5).

Note you could also solve the problem by considering choosing the 5 students one at a time.

the probability that the first student chosen is not a mechanical engineering major is 91/140;
the probability that the second student chosen is not a mechanical engineering major is 90/139;
the probability that the third student chosen is not a mechanical engineering major is 89/138;
the probability that the fourth student chosen is not a mechanical engineering major is 88/137;
the probability that the fifth student chosen is not a mechanical engineering major is 87/136

The probability that none of the 5 is a mechanical engineering student is

which is the same calculation as before.

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