Example Card: Finding Probability Using the Complement
Calculate the probability of an event using the complement rule: P(A) = 1 - P(not A), simplifying problems where the complement is easier to compute in Grade 9 statistics.
Key Concepts
Sometimes it's easier to calculate the probability of an event not happening. Let's find the chance a dart misses the bullseye on a target.
Example Problem A target consists of two concentric circles. The outer circle has a radius of 10 inches, and the inner bullseye has a radius of 2 inches. What is the probability a dart that hits the target does not land in the bullseye?
Step by Step 1. We will find the probability of the complement event. The key idea here is that the probability of not hitting the bullseye is $1$ minus the probability of hitting it. $$ \operatorname{P}(\text{not bullseye}) = 1 \operatorname{P}(\text{bullseye}) $$ 2. First, find the probability of hitting the bullseye, which is the ratio of the bullseye's area to the total target area. $$ \operatorname{P}(\text{bullseye}) = \frac{\text{area of bullseye}}{\text{area of target}} $$ 3. Use the area formula for a circle, $A = \pi r^2$. $$ = \frac{\pi(2)^2}{\pi(10)^2} $$ 4. Simplify the powers and the fraction. The $\pi$ terms cancel out. $$ = \frac{4\pi}{100\pi} = \frac{4}{100} = \frac{1}{25} $$ 5. Now, subtract this probability from $1$ to find the probability of not hitting the bullseye. $$ = 1 \frac{1}{25} = \frac{24}{25} $$.
Common Questions
What is Example Card: Finding Probability Using the Complement?
Example Card: Finding Probability Using the Complement is a key concept in Grade 9 math. It involves applying specific rules and properties to simplify expressions, solve equations, or analyze mathematical relationships. Understanding this topic builds foundational skills needed for higher-level algebra and beyond.
How is Example Card: Finding Probability Using the Complement used in real-world applications?
Example Card: Finding Probability Using the Complement appears in practical contexts such as financial calculations, engineering problems, and data analysis. Mastering this skill helps students model and solve problems they will encounter in science, technology, and everyday decision-making situations.
What are common mistakes when working with Example Card: Finding Probability Using the Complement?
Common errors include forgetting to apply rules to all terms, sign errors when working with negatives, and skipping verification steps. Always double-check by substituting answers back into the original problem and reviewing each algebraic step carefully.