Question

For certain population of students in university, the total students for first,
second and third semester listed according to the faculty, are shown in the
Table 1 below:
Table 1: Total students
Faculty Semester
First Semester Second Semester Third Semester
Engineering 200 150 350
Business 320 110 270
Education 400 340 360

(a) If a students is selected at random, find :
i. The probability of the students from the engineering faculty.

ii. The probability of the students second semester and from
education faculty.

iii. The probability that students from business faculty given that the
students third semester.

Answer 1

Answer on Question #64234 – Math – Statistics and Probability

Question

For certain population of students in university, the total students for first, second and third semester listed according to the faculty, are shown in the Table 1 below:

Table 1: Total students

Faculty Semester

(a) If a student is selected at random, find :

i. The probability of the student from the engineering faculty.

ii. The probability of the student's second semester and from education faculty.

iii. The probability that students from business faculty given that the student's third semester.

Solution

(i) $P(\text{Engineering faculty}) = \frac{200 + 150 + 350}{2500} = \frac{700}{2500} = 0.28.$

(ii) $P(\text{Second semester}, \text{Education faculty}) = \frac{340}{2500} = 0.136.$

(iii) $P(\text{Business faculty} | \text{Third semester}) = \frac{P(\text{Business faculty} | \text{Third semester})}{P(\text{Third semester})} = \frac{270}{980} \approx 0.2755$

Answer: (i) 0.28; (ii) 0.136; (iii) 0.2755.

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