Question

if a spinner has 10 equal-sized sections, which of the following will be false?
a. p(1) = 10% \t\t\t\tc. p(2) = 10%
b. p(not 1) = 10% \t\t\td. p(not odd) = 50%

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

Step1: Analyze Option A

The spinner has 10 equal - sized sections. The probability of landing on 1, \(P(1)=\frac{\text{Number of sections with 1}}{\text{Total number of sections}}\). Since there is 1 section with 1, \(P(1)=\frac{1}{10} = 0.1=10\%\). So option A is true.

Step2: Analyze Option B

The probability of an event and its complement sum to 1. The complement of \(P(1)\) is \(P(\text{not }1)\). We know that \(P(1) = 0.1\), so \(P(\text{not }1)=1 - P(1)=1 - 0.1 = 0.9 = 90\%
eq10\%\). So option B is false.

Step3: Analyze Option C (for completeness)

The probability of landing on 2, \(P(2)=\frac{\text{Number of sections with 2}}{\text{Total number of sections}}\). Assuming there is 1 section with 2, \(P(2)=\frac{1}{10}=0.1 = 10\%\). So option C is true.

Step4: Analyze Option D (for completeness)

The odd numbers from 1 to 10 are 1, 3, 5, 7, 9 (5 numbers). The non - odd (even) numbers are 2, 4, 6, 8, 10 (5 numbers). So \(P(\text{not odd})=\frac{\text{Number of non - odd sections}}{\text{Total number of sections}}=\frac{5}{10}=0.5 = 50\%\). So option D is true.

Answer:

B