A GMAC MBA new-matriculants survey provided the following data for 2018 students

Question

A GMAC MBA new-matriculants survey provided the following data for 2018 students. Applied to More Than One School Yes 207 299 185 No 23 and under 24-26 27-30 31-35 36 and over 201 379 268 193 169 Age Group a. Given that a person applied to more than one school, what is the probability that the person is 24-26 years old (to 2 decimals)? b. Given that a person is in the 36-and-over age group, what is the probability that the person applied to more than one school (to 4 decimals)? c. What is the probability that a person is 24-26 years old or applied to more than one school (to 4 decimals)? d. Suppose a person is known to have applied to only one school. What is the probability that the person is 31 or more years old (to 4 decimals)? e. Is the number of schools applied to independent of age? Select

Explanation / Answer

a)

P(person is 24-26 years old | person applied to more than one school)

= P(person is 24-26 years old and the person applied to more than one school) / P(the person applied to more than one school)

= (299 / 2018) / [(207+299+185+66+51) / 2018] = 299 / 808 = 0.37

b)

P(person applied to more than one school | person belongs to 36 and over age group)

= P(person applied to more than one school and the person belongs to 36 and over age group) / P(person belongs to 36 and over age group)

= (51 / 2018) / [(51+169) / 2018] = 51 / 220 = 0.2318

c)

P(person is 24-26 years old or applied to more than one school)

= P(person is 24-26 years old) + P(applied to more than one school) - P(P(person is 24-26 years old and applied to more than one school)

= [(299+379) / 2018] + [(207+299+185+66+51) / 2018] - [299 / 2018] = (678 + 808 - 299) / 2018 = 1187 / 2018 = 0.5882

d)

P(person is 31 years old or more | person applied to only one school)

= P(person is 31 years old or more and the person has applied to only one school) / P(the person applied to only one school)

= [(193+169) / 2018] / [(201+379+268+193+169) / 2018] = 362 / 1210 = 0.2992

e)

Now, P(person is aged 24-26) = (299 + 379) / 2018 = 678 / 2018

P(person applied to more than one school) = (207+299+185+66+51) / 2018 = 808 / 2018

Now, P(person is aged 24-26 and person applied to more than one school) = 299 / 2018

We can see that P(person is aged 24-26 and person applied to more than one school) is not equal to P(person is aged 24-26) . P(person applied to more than one school)

Hence they are not independent.

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