Probability and Statistics Final Review – Step-by-Step Guidance

Q16. The spinner at the right is spun 1 time. Find each of the following probabilities:

• a) $P(2 \text{ or } 3)$

• b) $P(\text{even or a 3})$

• c) $P(\text{a prime and an even number})$

Background

Topic: Basic Probability (Discrete Sample Space)

This question tests your understanding of calculating probabilities for simple events using a spinner with equally likely outcomes. You need to identify relevant outcomes and use the probability formula for discrete events.

Key Terms and Formulas

• Sample Space ($S$): The set of all possible outcomes. Here, $S = \{1, 2, 3, 4, 5, 6, 7, 8\}$.

• Probability of an event ($P(E)$): $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

• Even numbers: Numbers divisible by 2 (here: 2, 4, 6, 8).

• Prime numbers: Numbers greater than 1 with only two positive divisors (here: 2, 3, 5, 7).

Step-by-Step Guidance

1. List all possible outcomes for the spinner: $\{1, 2, 3, 4, 5, 6, 7, 8\}$.

2. For part (a), identify the outcomes for "2 or 3": $\{2, 3\}$.

3. For part (b), identify all even numbers (2, 4, 6, 8) and add 3 if it's not already included. List all outcomes for "even or a 3": $\{2, 3, 4, 6, 8\}$.

4. For part (c), identify numbers that are both prime and even. Recall that 2 is the only even prime number in the sample space.

5. For each part, use the probability formula: $P(E) = \frac{\text{Number of favorable outcomes}}{8}$ (since there are 8 sections).

Try solving on your own before revealing the answer!

Final Answers:

• a) $P(2 \text{ or } 3) = \frac{2}{8} = 0.25$

• b) $P(\text{even or a 3}) = \frac{5}{8} = 0.625$

• c) $P(\text{a prime and an even number}) = \frac{1}{8} = 0.125$

Each probability is calculated by counting the relevant outcomes and dividing by the total number of sections (8).