Question

One of your older friends is a student advisor to seniors at the UW’s Foster School of Business. She has determined the probability a student registers for a quantitative course (i.e., fin, acct) equals 0.37. She has also determined the probability a student registers for a qualitative course (i.e., mgmt, mktg) equals 0.61, and the probability a student registers for a qualitative course, given that she has already registered for a quantitative course, equals 0.82.(SHOW WORK;Round to 4 decimal places)

a)

Determine the probability a student registers for both quantitative and a qualitative course.

b)

Determine the probability a student registers for either quantitative or qualitative course.

c)

Determine the probability a student registers for a quantitative course, given she has registered for a qualitative course

d)

Determine the probability a student registers for a qualitative course, given she did NOT register for a quantitative course.

e)

Are the two events, registering for a quantitative course and registering for a qualitative course,mutually exclusive?

f)

Are the two events, registering for a quantitative course and registering for a qualitative course, statistically independent?

Answer 1

We would be looking at the first 4 parts here as:

We are given here that:
P( quantitative course) = 0.37,
P( qualitative course) = 0.61,
Also, we are given here that:
P( qualitative | quantitative) = 0.82

a) Using Bayes theorem, we get here:
P( quantitative and qualitative ) = P( qualitative | quantitative) P( quantitative course)

= 0.82*0.37 = 0.3034

Therefore 0.3034 is the required probability here.

b) Using addition law of probability, we get here:
P( quantitative or qualitative) = P( quantitative course) + P( qualitative course) - P( quantitative and qualitative )

= 0.37 + 0.61 - 0.3034

= 0.6766

therefore 0.6766 is the required probability here.

c) The probability here is computed using Bayes theorem as:

P( quantitative | qualitative) = P( quantitative and qualitative ) / P( qualitative course)

= 0.3034 / 0.61

= 0.4974

Therefore 0.4974 is the required probability here.

d)  Probability that a student registers for a qualitative course, given she did NOT register for a quantitative course.

P( qualitative | no quantitative ) = P(qualitative and no quantitative) / P(no quantitative)

= [ P(qualitative) - P(qualitative and quantitative) ] / 1 - P(quantitative)

= [ 0.61 - 0.3034] / (1 - 0.37)

= 0.4867

Therefore 0.4867 is the required probability here.