9. 假設投擲某金幣一枚出現正面與反面的機率皆為，試問平均要連擲幾次金幣，才會出現連續三次正面？

四、試題設計：請仔細閱讀以下文章後，設計符合新式學測的混合題題組（共四小題），並提供答案。出題類型需包含選擇題、填充題、簡答題、整合歸納題型等。文章內容無須改寫。共 24 分。 Social emotional learning (SEL) is a methodology that helps students of all ages to better comprehend their emotions, to feel those emotions fully, and demonstrate empathy for others. These learned behaviors are then used to help students make positive, responsible decisions, create frameworks to achieve their goals, and build positive relationships with others. According to the Collaborative for Academic, Social, and Emotional Learning (CASEL), an organization devoted to students and educators to help achieve positive outcomes for PreK-12 students, SEL involves five core competencies that can be applied in both the classroom, at home, and in students’ communities. These five core competencies are: Self-awareness To recognize your emotions and how they impact your behavior; acknowledging your strengths and weaknesses to better gain confidence in your abilities. Self-management To take control and ownership of your thoughts, emotions, and actions in various situations, as well as setting and working toward goals. Social awareness The ability to put yourself in the shoes of another person who may be from a different background or culture from the one you grew up with. To act with empathy and in an ethical manner within your home, school, and community. Relationship skills The ability to build and maintain healthy relationships with people from a diverse range of backgrounds. This competency focuses on listening to and being able to communicate with others, peacefully resolving conflict, and knowing when to ask for or offer help. Making responsible decisions Choosing how to act or respond to a situation is based on learned behaviors such as ethics, safety, weighing consequences, and the well-being of others, as well as yourself. While SEL isn’t a designated subject like history or math, it can be woven into the fabric of a school’s curriculum. There are several different approaches to SEL. Some teachers have a more formally designated portion of the school day devoted to SEL — sometimes taught in homeroom. These lessons become a recurring theme throughout the rest of the school day to help make the core competencies of SEL more real to students. Teachers may want to have students journal or write about their thoughts and feelings on a particular SEL lesson, or even have younger students partner with an older “buddy classroom” (or vice versa) to help students across different age levels bond or find common ground. Other teachers work SEL-related lessons into more formal subjects, like math, history, or reading. For instance, examples of SEL-in-action can include assigning a group project where students self-delegate roles to work together for the good of the group, role playing as historical figures to understand the rationale behind a person’s actions, or for students to conduct formal interviews with one another to take a pulse-check on current events. Teachers can also work with students to set goals in areas where they may need improvement and help chart their progress, giving them a measurable way to show their achievement and feel a sense of accomplishment. SEL is beneficial to both children and adults, increasing self-awareness, academic achievement, and positive behaviors both in and out of the classroom. From an academic standpoint, students who participated in SEL programs saw an 11 percentile increase in their overall grades and better attendance. On a more individual level, the skills learned within an SEL program have been shown to help students better cope with emotional stress, solve problems, and avoid peer pressure to engage in harmful activities. This can help set these students up for success throughout their school years and beyond

9. 假設投擲某金幣一枚出現正面與反面的機率皆為，試問平均要連擲幾次金幣，才會出現連續三次正面？

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