Question

The 13 -member math club needs to choose a student government representative. They decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Samara, who is a member of the club but NOT an officer, will be chosen? A. 0 B. \(\frac{1}{13}\) C. \(\frac{1}{10}\) D. \(\frac{3}{13}\) E. \(\frac{1}{3}\)

Short answer

Answer: C. \(\frac{1}{10}\)

Step-by-step solution

Determine the total number of possible outcomes

There are 13 members in the club, but 3 of them cannot be chosen, which leaves 10 members who can be chosen as representative. So there are 10 possible outcomes.

Determine the number of successful outcomes

Samara is just one person, so there is only one successful outcome, which is Samara being chosen.

Calculate the probability

We now have the total number of possible outcomes (10) and the number of successful outcomes (1). Using the Probability formula, we can find the probability of Samara being chosen: \(P = \frac{1}{10}\) So, the correct answer is: C. \(\frac{1}{10}\)

Key concepts

Understanding Roles in a Math Club

In a math club, membership extends beyond attending meetings and engaging in math problems. Certain members may hold specific roles, such as officers or representatives. These roles come with additional responsibilities, such as organizing events or representing the club in a larger student government.

In the context of probability calculations, when given a scenario to determine the likelihood of a member becoming a representative, it becomes crucial to understand the structure of the club. For instance, if officers are ineligible for selection, they must be excluded from the pool of potential candidates, thereby influencing the probability outcome.

For Samara's case, the math is straightforward: \[\begin{equation}P(\text{Samara chosen}) = \frac{\text{Number of ways Samara can be chosen}}{\text{Total number of eligible members}} = \frac{1}{10}\text{.}\text{\end{equation}\]} Understanding these roles and how they play into the odds of being selected allows students to better interpret such probability questions.

Student Government Elections

Student government elections are significant democratic exercises within schools. Students campaign for various positions, presenting their ideas and advocating for changes they wish to see. These elections teach practical life skills, such as public speaking, policy understanding, and negotiation.

When examining these elections through the lens of mathematics, probability becomes an interesting aspect to consider. One may calculate the likelihood of winning an election based on the number of candidates and assume that each candidate has an equal chance of being elected, although in reality, many factors could affect the outcome.

Numerical Illustration of Elections

In a simplified mathematical model, like the one involving Samara and the math club representative position, calculating these odds requires identifying eligible candidates and potential outcomes, just as we identify possible electoral outcomes in a student government scenario.

ACT Mathematics Preparation

Preparation for the ACT mathematics section is a comprehensive process that involves practicing a variety of topics, including algebra, geometry, and probability. Probability questions, such as the one Samara faces, are common on the ACT. They test a student's ability to analyze a situation, determine possible outcomes, and use mathematical formulas to calculate probabilities.

Students preparing for the ACT should familiarize themselves with the fundamentals of probability, including concepts like outcomes, events, and the basic probability formula: \[\begin{equation} P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}.\text{\end{equation}\]} A strong understanding of these concepts, paired with regular practice, can greatly aid in securing a strong score in the ACT math section. Furthermore, engaging in math clubs and other activities enriches learning, offering practical applications of these mathematical principles.