In a fictional stats class, 40% of students are female, and the rest are male. Of the female students, 30% are less than 20 years old and 90% are less than 30 years old. Of the male students, half are less than 20 years old and 70% are less than 30 years old. Make a contingency table to describe these two variables Find the probability that a randomly selected studet is 30 years or older If a student is 20 years or older, what is the probability that the student is female? If a student is less than 30 years old, what is the probability that the student is 20 years or older?

Diego Barr 2022-10-20 Answered
Problem:
In a fictional stats class, 40% of students are female, and the rest are male. Of the female students, 30% are less than 20 years old and 90% are less than 30 years old. Of the male students, half are less than 20 years old and 70% are less than 30 years old.
(a) Make a contingency table to describe these two variables
(b) Find the probability that a randomly selected studet is 30 years or older
(c) If a student is 20 years or older, what is the probability that the student is female?
(d) If a student is less than 30 years old, what is the probability that the student is 20 years or older?
My Thoughts:
(b) P(<30 years) = 1 - 0.78 = 0.22
(c) What I first did was find P(S2 given 'not A1'), but the answer doesn't make sense because the denominator ended up being smaller than the nominator.
(d) Do I solve this problem by doing 'not 20 years'?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

bigfreakystargl
Answered 2022-10-21 Author has 23 answers
Let F denote female; let M denote male; let A denote age.
Since 40% of the students are female and 30% of them are less than 20 years old, the probability that a student is female and less than 20 years old is
P ( F   A < 20 ) = P ( F ) P ( A < 20 F ) = 0.40 0.30 = 0.12
Since 90% of the female students are less than 30 years old, the probability that a student is female and less than 30 years old is
P ( F   A < 30 ) = P ( F ) P ( A < 30 F ) = 0.40 0.90 = 0.36
The probability that a student is female, at least 20 years old, and less than 30 years old can be found by subtracting the probability that she is less than 20 years old from the probability that she is less than 30 years old, which yields
P ( F   20 A 30 ) = P ( F   A < 30 ) P ( F   A < 20 ) = 0.36 0.12 = 0.24
Finally, the probability that a student is female and at least 30 years old is found by subtracting the probability that a student is female and less than 30 years old from the probability that a student is female, which yields
P ( F   A 30 ) = P ( F ) P ( F   A < 30 ) = 0.40 0.36 = 0.04
By using similar reasoning, we can fill in the table for the male students.
A < 20 20 A < 30 A 30 T o t a l F 0.12 0.24 0.04 0.40 M 0.30 0.12 0.18 0.60 T o t a l 0.42 0.36 0.22 1
The probability that a student is at least 30 years old is stated in the contingency table.
To find the probability that a student who is at least 20 years old is female, divide the probability that a female student is at least 20 years old by the probability that a student is at least 20 years old, both of which can be found by adding the appropriate columns in the table.
The probability that a student who is less than 30 years old is at least 20 years old can be found by subtracting the probability that the student is less than 20 years old from the probability the student is less than 30 years old. To find the probability that a student is less than 30 years old, you can subtract the probability that a student is greater than 30 years old from 1.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-11-19
why doubling the number in a contingency table changes the p-value?
i am doing a facts trouble, which is checking out if the evaluation of someone is impartial of the individual's intercourse. i'm given a contingency desk, I calculated the expected fee for each access and calculated the chi-rectangular value then I got a p-fee.
Then the query requested me to do the same thing after doubling all entries in the contingency desk, I were given a p-price smaller than the only I got earlier than. Why does this take place? Can all and sundry supply me an cause of the distinction?
asked 2022-11-21
A survey was carried out to find out if the occurrence of different kinds of natural disasters varies from on part of the town to the other. The town was divided into two as center town and town outskirts, and the natural disasters were divided into tornadoes, lighting, and fires.The survey showed these results:
Tornadoe Lightning Fires
Town Center 10 220 120
Town Outskirts 20 150 200
Do the above findings provide enough proof at 95 confidence level to indicate that the happening of natural disasters depends on the part of town?
asked 2022-10-17
Is my answer correct? Are these two events independent?
A B C 78 520 D 156 56
This is a contingency table and the question is if D is independent of A.
Now I know that if they are, then P ( A D ) = P ( A ) P ( D )
So in my case, P ( A D ) = 156 810
P ( A ) = 234 810
P ( D ) = 212 810
P ( A D ) = 0.19
P ( A ) P ( D ) = 0.07
asked 2022-11-05
Mary is certainly one of medical doctor Brown's patients. She has carried out a domestic pregnancy take a look at which has given a high quality end result. what's the possibility that the pregnancy take a look at used by doctor Brown in his surgical procedure will say Mary is pregnant given that the home check became nice?
Home pregnancy test is 85% accurate
Doctor Brown pregnancy test is 95% accurate
20 females are pregnant and 80 females are not
asked 2022-10-15
Why is the expected frequency during a chi square dependence test calculated the way that it is?
I understand the chi square test for testing whether or not a certain model is appropriate. I understand the process based upon which we pick the expected values. But, when it comes to the dependence test (the one where we use a contingency table), I don't understand why the expected frequency is calculated from the observed frequencies in the contingency table using (row total x column total)/grand total.
Someone please explain.
asked 2022-10-18
Is responses in statistics the equivalent to random variables in probability?
The focus of this class is multivariate analysis of discrete data. The modern statistical inference has many approaches/models for discrete data. We will learn the basic principles of statistical methods and discuss issues relevant for the analysis of Poisson counts of some discrete distribution, cross-classified table of counts, (i.e., contingency tables), binary responses such as success/failure records, questionnaire items, judge's ratings, etc. Our goal is to build a sound foundation that will then allow you to more easily explore and learn many other relevant methods that are being used to analyze real life data. This will be done roughly at the introductory level of the first part of the required textbook by A. Agresti (2013), which covers a superset of A. Agresti (2007)
in which, is responses here (statistics) the equivalent to random variables in probability
another page in that site says
Discretely measured responses can be:
Nominal (unordered) variables, e.g., gender, ethnic background, religious or political affiliation
Ordinal (ordered) variables, e.g., grade levels, income levels, school grades
Discrete interval variables with only a few values, e.g., number of times married
Continuous variables grouped into small number of categories, e.g., income grouped into subsets, blood pressure levels (normal, high-normal etc)
We we learn and evaluate mostly parametric models for these responses.
are variables and responses interchangeable here?
asked 2022-10-30
i am seeking to solve a query regarding contingency table as a ways as I know contingency desk display matter no longer densities,and i am having difficult time comprehending this simple desk. My tries turned into basically calculating the marginal distribution however the possibilities failed to sum to one. for example I tried solving the first question via:
P ( A , B ) = ( P ( A , B , C ) d C
but I'm missing something is dC probabilities or just count?