In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.
If a student is chosen at random what is the probability they are:
a civil engineering major? 1 (Format: decimal 0.XX)
a civil enginering major or mechanical engineering major?
a general engineering major?
not a computer science major?
Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?
For the first one, 13% are Civil Engineers, but where do I go from there?
Probability is not a percentage. Change format to decimal.
Either-or probabilities are found by adding the individual probabilities.
General = (100-30-49-13)/100 = ?
Not computer = (100-30)/100 = ?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
5 not mech = [(100-49)/100]^5 = ?
To find the probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.
Given the information,
- Total number of students in the class = 100
- Computer science majors = 30
- Mechanical engineering majors = 49
- Civil engineering majors = 13
- Rest are general engineering majors
1. Probability of being a civil engineering major:
Number of civil engineering majors = 13
Probability = Number of civil engineering majors / Total number of students
Probability = 13 / 100
Probability = 0.13
2. Probability of being a civil engineering major or mechanical engineering major:
Number of civil engineering majors = 13
Number of mechanical engineering majors = 49
Total = Number of civil engineering majors + Number of mechanical engineering majors
Probability = Total / Total number of students
Probability = (13 + 49) / 100
Probability = 62 / 100
Probability = 0.62
3. Probability of being a general engineering major:
Number of general engineering majors = Total number of students - (Number of computer science majors + Number of mechanical engineering majors + Number of civil engineering majors)
Number of general engineering majors = 100 - (30 + 49 + 13)
Number of general engineering majors = 100 - 92
Number of general engineering majors = 8
Probability = Number of general engineering majors / Total number of students
Probability = 8 / 100
Probability = 0.08
4. Probability of not being a computer science major:
Number of non-computer science majors = Total number of students - Number of computer science majors
Number of non-computer science majors = 100 - 30
Number of non-computer science majors = 70
Probability = Number of non-computer science majors / Total number of students
Probability = 70 / 100
Probability = 0.7
Now, let's calculate the probability that none of the five randomly chosen students are mechanical engineering majors.
Number of mechanical engineering majors = 49
Number of non-mechanical engineering majors = Total number of students - Number of mechanical engineering majors
Number of non-mechanical engineering majors = 100 - 49
Number of non-mechanical engineering majors = 51
Probability of none being mechanical engineering majors:
We need to consider the probability for each student, assuming independence in the selection.
For the first student: Probability of not being a mechanical engineering major = Number of non-mechanical engineering majors / Total number of students = 51 / 100
For the second student: Probability of not being a mechanical engineering major = Number of non-mechanical engineering majors / Total number of remaining students = 51 / 99
For the third student: Probability of not being a mechanical engineering major = Number of non-mechanical engineering majors / Total number of remaining students = 51 / 98
For the fourth student: Probability of not being a mechanical engineering major = Number of non-mechanical engineering majors / Total number of remaining students = 51 / 97
For the fifth student: Probability of not being a mechanical engineering major = Number of non-mechanical engineering majors / Total number of remaining students = 51 / 96
Probability of none being mechanical engineering majors = (51/100) * (51/99) * (51/98) * (51/97) * (51/96)
Note: This calculation assumes that the selection process is done without replacement.
I hope this helps! Let me know if you have any further questions.
To calculate the probabilities, we need to use the concept of relative frequency. The relative frequency is calculated by dividing the number of outcomes of interest by the total number of possible outcomes.
1. Probability of being a civil engineering major:
There are 13 civil engineering majors out of a total of 100 students, so the probability is:
13/100 = 0.13
2. Probability of being a civil engineering major or mechanical engineering major:
There are 49 mechanical engineering majors and 13 civil engineering majors. Since these two groups are mutually exclusive (i.e., a student cannot be both a mechanical and civil engineering major simultaneously), we can add the number of students from each group to get the total number of students in either of the two majors:
49 + 13 = 62
So, the probability is:
62/100 = 0.62
3. Probability of being a general engineering major:
Since the total number of students is 100 and we know the number of students from other majors, we can calculate the number of general engineering majors:
Total students - (Computer Science majors + Mechanical Engineering majors + Civil Engineering majors)
100 - (30 + 49 + 13) = 8
Therefore, the probability is:
8/100 = 0.08
4. Probability of not being a computer science major:
We know there are 30 computer science majors out of 100 students, so the probability of not being a computer science major is:
(100 - 30)/100 = 70/100 = 0.70
Now, let's move on to the second part of the question:
To calculate the probability that none of the five randomly chosen students are mechanical engineering majors, we need to calculate the probability that each individual student is not a mechanical engineering major, and then multiply these probabilities together.
Probability of one student not being a mechanical engineering major:
Total students - Mechanical Engineering majors = 100 - 49 = 51
Probability of one student not being a mechanical engineering major = 51/100
Probability that none of the five chosen students are mechanical engineering majors:
(51/100) * (51/100) * (51/100) * (51/100) * (51/100) = (51/100)^5 ≈ 0.0988
Therefore, the probability that none of the five randomly chosen students are mechanical engineering majors is approximately 0.0988.