The beverage that the people prefer to drink in the morning are shown in the Venn diagram to the right. Which of the following Venn diagram visually represents the people that do not drink coffee or tea?

Which diagram illustrates mutually exclusive events?

What is the set that contains all of the elements that are in at least one of the two events?

Which events have no outcome in common?

What is the difference between permutation and combination?

Ten students will be arranged in a row. Which counting technique will be used to find the number of ways it can be done?

Albert has three shirts and five caps. He wants to know in how many ways he can wear them to create different outfits. Which counting technique will help him?

What is the term used to refer to the outcomes of an experiment?

What refers to the product of the positive integer n and all the positive integers less than n?

Which uses circles to represent sets, in which the relationship between the sets is indicated by the arrangement of the circles?

What is referred to when two events occur independently, without affecting each other?

After the tryouts for the volleyball team, the coach selects 14 students to join the team. Due to a problem with transportation, only nine students can travel. In how many ways can the coach pick the people?

Which refers to the order of arrangement of objects where order does not matter?

A 10 - diamond card is drawn from a 52 deck of cards. Which of the following illustrates this event?

What does the notation 4C2 implies?

What will be the probability of getting odd numbers if a dice is thrown?

George and Aliyah are calculating the probability of selecting either a blue or red marble from a collection comprising eight blue marbles, six red marbles, eight yellow marbles, and four white marbles. Below are their respective solutions. Which one provides the accurate answer?

Which is the correct meaning of combination?

A multiple-choice test has 12 questions. Each question has six choices: A, B, C, D, E, or F. How many ways can the test be answered?

A toothpaste firm claims that in a survey of 54 people, they were using either Colgate, Hapee, or Close-up brand. The following statistics were found: six people used all three brands, five used only Hapee and Close-up, 18 used Hapee or Close-up, two used Hapee, two used only Hapee and Colgate, one used Close-up and Colgate, and 20 used only Colgate. Is the survey worth paying for?

Which situations involves permutation?

You are hired in a restaurant as a supervisor. Part of your job is to plan the menu to be served every day. You are tasked by the owner to come up with a recommendation of a list of different choices of food to be served. Your recommendation must include an explanation why some dishes are less or more frequently served. What mathematical concepts are used in this situation?

What is the arrangement of three books in English, mathematics, and science by 2’s on a shelf?

In which situation are the events mutually exclusive?

In a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and brown eyes. If a child is selected at random, what is the probability that the child has blonde hair or brown eyes?

Which scenario best illustrates mutually exclusive events?

The spinner shown on the right is divided into eight equal sectors. Elliott spins the spinner once. What is the probability that the pointer lands on an odd number or a blue sector?

In how many ways can a committee of seven students be chosen from nine juniors and nine seniors if there must be four seniors in the committee?

There are 15 juniors and 20 seniors in the Photography Club. The club is to send 7 representatives to the local student photography competitions. If the members of the club decide to send 3 juniors and 4 seniors, how many different groups are possible? Which of the following computations gives the correct answer?

Which statement/s is/are true?

I. Independent events can be disjoint.
II. If two events are not disjoint, then they must be independent.
III. If two events are independent, then they must not be disjoint.

Barangay Sampaloc Zone 1 is organizing Heart’s Week, an event for a cause. The proceeds will be donated to Heart Smile, a foundation that funds the medication of children with heart conditions. The barangay chairman is taking the lead in organizing various committees. The first committee is the planning committee. From a group of seven men and six women, five persons are to be selected to form the committee so that at least three men are there on the committee. How can the barangay chairman determine the possible number of committees where each member is equal in position?

Kudarat is the organizer of a basketball tournament in your barangay. He is to submit to the tournament head committee the budget for the referees’ fees. There are 12 teams who registered. He needs to decide what format of the game to follow so that the budget will be minimal. Which format will he recommend having minimal budget for referees’ fees based on the number of games played?

I. Follow the single round robin system and the team with the greatest number of wins becomes the champion.
II. Separate the 12 teams into two groups. Each group of six teams will play a single round robin. The greatest number of wins per group will play for the championship in a best of three.

In a small assembly plant with 50 employees, each worker is expected to complete work assignments on time and in such a way that the assembled product will pass a final inspection. On occasion, some of the workers fail to meet the performance standards by completing work late or assembling a defective product. At the end of a performance evaluation period, the production manager found out that five of the 50 workers completed work late, six of the 50 workers assembled a defective product, and two of the 50 workers both completed work late and assembled a defective product. After reviewing the performance data, the production manager decided to assign a poor performance rating to any employee whose work was either late or defective. What is the probability that the production manager assigns an employee a poor performance rating? The problem involves what probability?

Tom and Jerry were assigned a challenging problem by their teacher. They were asked to solve this problem: In a primary election, there are four candidates for mayor, five candidates for city treasurer, and two candidates for county attorney. In how many ways may voters mark their ballots if they exercise their right not to vote in any or all of the races?

Tom’s approach: The total number of ways a voter can mark their ballot for all three offices would be 5 × 6 × 3 = 90.

Jerry’s Approach: Applying the multiplication principle, he calculated 4 × 5 × 2 = 40 ways in which a voter can mark their ballot for all three offices.

Which choice best reflect their understanding?