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: Calculate total number of outcomes

The spinner has 10 equal - sized sections numbered 1 - 10, so the total number of outcomes $n = 10$.

Step2: Analyze "spinning a number less than 3"

Numbers less than 3 are 1 and 2. So the number of favorable outcomes $m_1=2$. The probability $P_1=\frac{m_1}{n}=\frac{2}{10}=\frac{1}{5}$.

Step3: Analyze "spinning a 4 or 5"

The numbers 4 and 5 are 2 favorable outcomes. So the number of favorable outcomes $m_2 = 2$. The probability $P_2=\frac{m_2}{n}=\frac{2}{10}=\frac{1}{5}$.

Step4: Analyze "spinning an odd number"

Odd numbers are 1, 3, 5, 7, 9. So the number of favorable outcomes $m_3 = 5$. The probability $P_3=\frac{m_3}{n}=\frac{5}{10}=\frac{1}{2}$.

Step5: Analyze "spinning a number greater than 8"

Numbers greater than 8 are 9 and 10. So the number of favorable outcomes $m_4 = 2$. The probability $P_4=\frac{m_4}{n}=\frac{2}{10}=\frac{1}{5}$.

Step6: Analyze "spinning a number less than 8"

Numbers less than 8 are 1, 2, 3, 4, 5, 6, 7. So the number of favorable outcomes $m_5 = 7$. The probability $P_5=\frac{m_5}{n}=\frac{7}{10}$.

Answer:

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