Question

which event has theoretical probability of exactly \\(\frac{1}{5}\\)? select three options. spinning a number less than 3; spinning a 4 or 5; spinning an odd number; spinning a number greater than 8; spinning a number less than 8

Explanation:

Step1: Determine total outcomes

The spinner has numbers 1 - 10, so total outcomes \( n = 10 \). We need events with probability \( \frac{1}{5}=\frac{2}{10} \) (since probability \( P=\frac{\text{favorable outcomes}}{\text{total outcomes}} \), so favorable outcomes should be 2).

Step2: Analyze each event

• Spinning a number less than 3: Numbers are 1, 2. Favorable outcomes = 2. \( P=\frac{2}{10}=\frac{1}{5} \).
• Spinning a 4 or 5: Numbers are 4, 5. Favorable outcomes = 2. \( P=\frac{2}{10}=\frac{1}{5} \).
• Spinning an odd number: Odd numbers: 1, 3, 5, 7, 9. Favorable outcomes = 5. \( P=\frac{5}{10}=\frac{1}{2}

eq\frac{1}{5} \).

• Spinning a number greater than 8: Numbers are 9, 10. Favorable outcomes = 2. \( P=\frac{2}{10}=\frac{1}{5} \).
• Spinning a number less than 8: Numbers: 1 - 7. Favorable outcomes = 7. \( P=\frac{7}{10}

eq\frac{1}{5} \).

Answer:

spinning a number less than 3, spinning a 4 or 5, spinning a number greater than 8