# Conjuntos y Probabilidades: Ejemplo de una excelente tutoría de Estadística

Comentarios de la Tutora: La tutoría se llevo a cabo en el tiempo previsto para su resolución, utilizando el método propuesto por el estudiante y acompañándolo en el desarrollo del mismo. En todo momento se buscó que el estudiante se sintiera involucrado en el trabajo y entendiera qué se estaba haciendo.

La tutoría:

Student Question: Employment data at a large company reveal that 72% of workers are married, that 44% are college graduates, and that half of the college grads are married. What’s the probability that a randomly chosen worker is: a) neither married nor a college graduate? b) is married but not a college graduate? c) is married 9or a college graduate?

Tutor: Welcome! My name is Anahid. How are you?

Student: Good. U?

Tutor: I’m great! Thanks. Tell me, what can I do for you today?

Student: I have a entire assignment to do like the problem stated, and I’m not sure how to get it solved. I started with a contingency table, but that’s it…

Tutor: well done!

Student: that’s as far as i get….

Tutor: check that we also know the totals, how many of them are married?

well done!, check that married and not married must sum 100%
how many are not married?

Student: 56?

Tutor: well done!(but 56 is for not college)

Student: oh, sorry

Tutor: Very close — let’s take another look and see what we missed.
we are setting college graduates on the line
and married on the column

44% are college graduates

so 100%-44%=56% are not college graduates

Do you understand how we did that last part?

Student:  No
I do. the complimentary rule?

Tutor: that’s right!

Student: okay. I follow you now! 🙂

Tutor: let’s do the same with the married on the last column
72% are married, how much are not married?

Student: 28%

Tutor: Excellent!  You did that step perfectly.
Do you know what to do next?

Student: for college grad and not married, it would be 22%, is that correct?

Tutor: Perfect!  Good work.
what about for married and not college grad?

Student: 50%?

Tutor: Great job on that one! Nicely done.

Student: 😀

Tutor: can you complete the table?
You got it!

Student: yay!

Tutor: now we are ready to answer the questions

Student: okay

Tutor: how much is the answer on letter a?

Student: 6% ??

Tutor: well done!
what about letter b?

Student: 50%

Tutor: Perfect!  Good work.
what about the last one?

Student: 31.7%?
72% x44%?

Tutor: Very close — let’s take another look and see what we missed.
let’s focus on the center of the table

Student: okay

Tutor: can you circle the ones that are married?
well done!
what about the ones that are college graduates?
well done!
if we were to find the ones that are married OR college grad we should add all the circles
how much will that be?

Student: 94%?

Tutor: Great job on that one! Nicely done.
Does this problem make sense to you now?

Student: or = addition?

Tutor: yes, but be careful, we did not add 44% and 72%

Student: haha… too much!!!
because they could be married and not grad, grad and not married, and married or grad… all three are feasable choices!!??

Tutor: that’s right, but if we added 44%+72% we will be counting the 22% od the intersection twice

Student: I get it!!! Makes sense now!

Tutor: check that 44%+72%-22%=94%
Do you have any questions about anything we went over today?

Student: No, everything was great!. Very good explanation of everything! Have a good evening!

Tutor: Thank you, Have a good evening too!

Colaboradora: Anahid Bauer, Tutora Argentina de Estadística

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