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A certain small college runs two sections of MATH 101 every semester, one taught by Prof. A and the other by Prof. B. At the end of one semester, they both polled their classes to find out which part of the course students liked the most.


The data they collected is summarized in the following table and is then used to compute empirical probabilities concerning their students in other semesters.



Prof. A's class
Prefers Probability :36
Prefers Financial Mathematics :4

Prof. B's class
Prefers Probability:24
Prefers Financial Mathematics: 16

a) What is the probability that a student at this college who takes MATH 101 will take it with Prof. B and prefer Probability? (Round your answer, if necessary, to one decimal place.)

b) What is the probability that a student at this college who takes MATH 101 with Prof. B will prefer Probability? (Round your answer, if necessary, to one decimal place.)

c) What is the probability that a student at this college who takes MATH 101 and prefers Probability is taking the course with Prof. B? (Round your answer, if necessary, to one decimal place.)

Sagot :

Using the probability concept, it is found that:

a) 0.3 = 30% probability that a student at this college who takes MATH 101 will take it with Prof. B and prefer Probability.

b) 0.6 = 60% probability that a student at this college who takes MATH 101 with Prof. B will prefer Probability.

c) 0.4 = 40% probability that a student at this college who takes MATH 101 and prefers Probability is taking the course with Prof. B.

-------------------------

  • A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

  • Total of 36 + 4 + 24 + 16 = 80 students.
  • Of those, 24 take MATH 101 with Prof B. and prefer probability.

Thus:

[tex]p = \frac{24}{80} = 0.3[/tex]

0.3 = 30% probability that a student at this college who takes MATH 101 will take it with Prof. B and prefer Probability.

Item b:

  • 24 + 16 = 40 students that MATH 101 with Prof B.
  • Of those, 24 prefer probability.

Then:

[tex]p = \frac{24}{40} = 0.6[/tex]

0.6 = 60% probability that a student at this college who takes MATH 101 with Prof. B will prefer Probability.

Item c:

  • 36 + 24 = 60 students prefer probability.
  • Of those, 24 take the course with Prof. B.

Then:

[tex]p = \frac{24}{60} = 0.4[/tex]

0.4 = 40% probability that a student at this college who takes MATH 101 and prefers Probability is taking the course with Prof. B.

A similar problem is given at https://brainly.com/question/24658381

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