At a certain university in Western Canada, 42% of all 1st-year students are regi

Question

At a certain university in Western Canada, 42% of all 1st-year students are registered in an introductory Calculus course, 26% are registered in an introductory Economics course, and 62% are registered in an introductory Calculus or an introductory Economics course.

You randomly pick a 1st-year student from this particular university. Find the probability that the student chosen

Part (a) is registered in both an introductory Calculus course and an introductory Economics course.

Part (b) is registered in an introductory Calculus course and not registered in an introductory Economics course.

Part (c) is not registered in introductory Calculus or not registered in introductory Economics.

Part (d) is not registered in either course

Part (e) If a student is registered in introductory Calculus, what is the probability they are also registered in introductory Economics?

Part (f) iIf a student is not registered in introductory Economics, what is the probability they are also not registered in introductory Calculus?

Explanation / Answer

Here we are given that: 42% of all 1st-year students are registered in an introductory Calculus course, therefore we have here:

P( calculus ) = 0.42

Also, we have 26% are registered in an introductory Economics course, which means that:

P( economics ) = 0.26

Also we are given that: 62% are registered in an introductory Calculus or an introductory Economics course which means that:

P( calculus or economics ) = 0.62

a) Using the addition law of probability we get:

P( calculus and economics ) = P( calculus ) + P( economics ) - P( calculus or economics )

P( calculus and economics ) = 0.42 + 0.26 - 0.62 = 0.06

Therefore 0.06 is the required probability here.

b) Now the probability that the student chosen is registered in an introductory Calculus course and not registered in an introductory Economics course is computed as:

= P( calculus ) - P( calculus and economics )

= 0.42 - 0.06

= 0.36

Therefore 0.36 is the required probability here.

c) Probability that he is not registered for introductory Calculus or not registered in introductory Economics is computed as:

= 1 - P( calculus and economics ) = 1 - 0.06 = 0.94

Therefore 0.94 is the required probability here.

d) Probability that he is not registered in either course is computed as:

= 1 - P( calculus or economics ) = 1- 0.62 = 0.38

Therefore 0.38 is the required probability here.

e) Given that a student is registered in introductory Calculus, probability that he is also registered for the introductory Economics is computed using bayes theorem as:

= P( calculus and economics ) / P( calculus )

= 0.06 / 0.42

= 0.1429

Therefore 0.1429 is the required probability here.

f) Given that a student is not registered in introductory Economics, probability they are also not registered in introductory Calculus is computed as:

= P( not registered in both ) / P ( not registered for economics )

= 0.38 / [ 1- 0.26 ]

= 0.38 / 0.74

= 0.5135

Therefore 0.5135 is the required probability here.

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