Q3: The following frequency table shows the classification of 90 students in the

Question

Q3: The following frequency table shows the classification of 90 students in their sophomore year of college according to their understanding of physics, chemistry and mathematics. Physics Average Extensive Chemistry Chemistry Average Extensive Average Extensive 16 12 14 18 Mathematics Average 8 Extensive 14 4 If a student is selected at random, find the probability that the student has a) an extensive understanding of chemistry b) an extensive understanding of physics and an average understanding of mathematics and chemistry third; other two. c) an extensive understanding of any two subjects and an average understanding of the d) an extensive understanding of any one subject and an average understanding of the

Explanation / Answer

(a) Total number of students = 90

Number of students have extensive understanding of chemistry = 16+ 4 + 18 + 4 = 42

Pr(Extensive uderstanding of chemistry) = 42/90 = 0.4667

(b) Total number of studens having extensive understanding of physics and average understanding of mathematics = 12 + 18 = 30

Probability of such event = 30/90 = 0.333

(c) Total number of students having two subjects extensive understanding and an average understanding of the third.

(i) Extensive understanding of Chemistry and physics and average of mathematics = 18

(ii) Extensive understanding of Chemistry and mathematics and average of physics = 4

(iii) Extensive understanding of Mathematics and physics and average of chemistry = 14

so probability of such event = (18 + 4 + 14)/90 = 0.40

(d) Now identifying the number of student who have extensive understanding of any one subject and average understanding of the other two

(i) Extensive understanding of physics and average of other two = 12

(ii) Extensive understanding of chemistry and average of other two = 16

(iii) Extensive understanding of mathematics and average of other two = 14

Probability of such event then = (12 + 16 + 14)/90 = 0.4667

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