Contingency tables

In a study on social media use in a secondary school, 100 2nd year Bachillerato students were surveyed about their preferred platform. The data are shown in the following contingency table, although some values have been erased:

Given that there is a total of 45 boys and 55 girls:

1. a) Complete the missing values in the table.
2. b) If we choose a student at random, what is the probability that their preferred network is TikTok?
3. c) What is the probability that it is a girl who prefers Instagram?

A group of 200 teenagers was asked whether they have cereals or fruit for breakfast. The results were: 120 have cereals for breakfast, 100 have fruit for breakfast and 40 have both.

1. a) Complete the following contingency table to organise the data:

1. b) What is the probability that a teenager has neither cereals nor fruit for breakfast?
2. c) Given that a teenager has cereals for breakfast, what is the probability that they also have fruit for breakfast?

A survey on voting intention and main social concern (Environment, Economy or Health) was conducted, obtaining the following partial probability table:

1. a) Complete the contingency table.
2. b) Calculate the probability that a Party A voter is concerned about Health.
3. c) Are the events "Voting for Party B" and "Being concerned about the Environment" independent? Justify your answer mathematically.

In a padel tournament organised by the local council, 80 people participate. It is known that 32 are men and the rest women. Of the men, 20 are federated, whereas among the women only 12 are federated.

1. a) Organise the information in a contingency table.
2. b) If we select a participant at random, calculate the probability that they are not federated.
3. c) What is the probability that the participant is female, given that she is federated?

Observe the following table classifying a company's employees according to their department and whether they have requested remote working:

Calculate with reasoning using the table:

1. a) $P(T | V)$, the probability that an employee works remotely if they belong to the Sales department.
2. b) $P(I | T)$, the probability that an employee is from R&D given that they have requested remote working.
3. c) What is more likely: that a Sales employee works remotely or that an R&D employee works remotely?

A sports centre offers Yoga, Pilates and Crossfit classes. The distribution of the $300$ members by activity and age group is as follows:

1. a) If we choose a member at random, what is the probability that they practice Yoga or are Young?
2. b) Among Adult members, which activity is the most probable?
3. c) If a Crossfit practitioner is chosen, what is the probability that they are Young?

A survey was conducted on transport habits for going to university. $40\%$ of the students are male ($H$) and $60\%$ are female ($M$). $25\%$ of the males go by car ($C$), whereas $15\%$ of the females use this mode of transport.

1. a) Considering a sample of 100 people, construct the contingency table with absolute values.
2. b) Calculate the probability that a randomly chosen person is female and does not use a car.
3. c) Calculate the probability that, given they are male, they do not use a car.

You can do it on paper and send a photo with your answer.

In a study on digital content consumption habits among $200$ teenagers, it has been observed that $120$ are subscribed to a streaming platform. Of those who are subscribed, $80$ prefer watching series over films. Among those who do not pay for a subscription, $30$ prefer films.

1. a) Organise the above information in a contingency table.
2. b) If we choose a teenager at random, what is the probability that they prefer watching series?
3. c) Given that the chosen teenager prefers films, what is the probability that they are not subscribed to any platform?

The success of an advertising campaign on social media is analysed. Of the people who saw the ad, $40\%$ did so on Instagram and $60\%$ on TikTok. It is known that $15\%$ of those who saw it on Instagram bought the product, while on TikTok $10\%$ did.

1. a) Imagine a group of $1000$ people who have seen the ad and transfer these percentages to a contingency table (rows: buys / does not buy; columns: Instagram / TikTok, with their totals).

1. b) Calculate the probability that a randomly chosen person has bought the product.

1. c) Given that a person has bought the product, on which social network is it more likely that they saw the ad?

In a language academy, students are divided by level (Basic or Advanced) and by language (English or German). The probability of a student being in the advanced level is $0,4$. The probability of studying English is $0,7$. It is known that the probability of a student studying German and being at the basic level is $0,2$.

1. a) Draw up a contingency table with probabilities (where the total is $1$).
2. b) Calculate the probability that a randomly chosen student is at the advanced level and studies English.
3. c) If a student studies English, what is the probability that they are at the basic level?

A technology company analyses the relationship between the use of a new model of wireless headphones and customer satisfaction. Of the $500$ users surveyed, $350$ bought the "Pro" model and the rest the "Basic" model. It is known that event $S$ (being satisfied) and event $M$ (Pro model) are independent. If the probability of being satisfied is $P(S) = 0,8$:

1. a) Complete the contingency table with the expected number of people for each category.
2. b) Calculate the probability that a user bought the "Basic" model and is not satisfied.
3. c) What does it mean in this context for the events to be independent?

A vocational college offers two higher-level courses: Web Application Development ($DAW$) and Marketing and Advertising ($MK$). $55\%$ of the students are enrolled in $DAW$.

It has been found that $20\%$ of the students in $DAW$ and $15\%$ of those in $MK$ drop out of their studies before finishing the first year.

1. a) Construct the contingency table associated with this educational centre.

1. b) If we choose a student at random from among those who dropped out of the course, what is the probability that they were enrolled in Marketing and Advertising?

1. c) Is dropping out of studies independent of the course in which the student is enrolled? Reason your answer by comparing $P(Abandono)$ with $P(Abandono | DAW)$.

You can do it on paper and send a photo with your answer.