LESSON T-1 Understand Likelihood and Probability The probabily of an will occur. The likelihood likelihood of an eve common descriptions are likely or unlikely. A sample space is the set of all possible outcomes. An event is a single outcome or group of outcomes. An outcome is a possible result of an action. Probability can be represented as a fraction, as a decimal, or as a percent. Something is fair if there is an equal chance for each outcome to occur. Practice 1. Antonio rolls the 10 -sided die from the example. What is the probability of rolling a number 10 or less? a number greater than 10 ?. 2. A spinner with 8 equal-sized sections is used for a game. Based on the descriptions below, is the spinner fair? Explain. The probability the pointer will land on yellow is 1 out of 4.The probability the pointer will land on blue is 2 out of 8 . The probabilities that the pointer will land on green or red are both \( 25 \% \). SON 7-2 Understand Theoretical Probability Quick Review Practice

1. Antonio rolls a 10‑sided die, so the sample space is \[ S = \{1, 2, 3, \dots, 10\}. \] - The probability of rolling a number 10 or less is calculated by using the formula \[ P(\text{number } \leq 10) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}. \] Since every outcome is 10 or less, we have \[ P(\text{number } \leq 10) = \frac{10}{10} = 1. \] - The probability of rolling a number greater than 10 is \[ P(\text{number } > 10) = \frac{0}{10} = 0. \] 2. The spinner has 8 equal-sized sections, meaning each section has an equal probability of \[ \frac{1}{8} = 12.5\% \] if each section were equally likely. However, the given probabilities are described in terms of color: - Yellow: \( P(\text{yellow}) = \frac{1}{4} = 25\% \). - Blue: \( P(\text{blue}) = \frac{2}{8} = 25\% \). - Green: \( 25\% \). - Red: \( 25\% \). When adding these probabilities, we have \[ 25\% + 25\% + 25\% + 25\% = 100\%. \] To determine if the spinner is fair, we compare the given probabilities with the natural probability based on 8 equal sections. Each 25% probability corresponds to \[ 0.25 \times 8 = 2 \] sections. That is, yellow occupies 2 sections, blue occupies 2 sections, green occupies 2 sections, and red occupies 2 sections. Since all colors have the same probability and the sections are equal in size, the spinner is fair.