Question

the spinner is equally likely to land on any of the six sections.

what is the probability that the spinner will land on a number greater than 4 or on a shaded section?

\\(\frac{2}{9}\\)
\\(\frac{1}{2}\\)
\\(\frac{2}{3}\\)
\\(\frac{5}{6}\\)

Explanation:

Identify the sample space and outcomes

Using the Theoretical Probability knowledge point
The spinner has six equally likely sections numbered 1 through 6.

$$ S = \{1, 2, 3, 4, 5, 6\}, \quad n(S) = 6 $$

Define the events and their outcomes

Using the Theoretical Probability knowledge point
Let event \(A\) be landing on a number greater than 4:

$$ A = \{5, 6\} $$

Let event \(B\) be landing on a shaded section. Looking at the spinner, the shaded sections are labeled 1, 3, and 5:

$$ B = \{1, 3, 5\} $$

Find the intersection of the events

Using the Non-Mutually Exclusive Events knowledge point
Identify the outcomes that belong to both event \(A\) and event \(B\):

$$ A \cap B = \{5\} $$

Apply the probability addition rule

Using the Probability Addition Rule and Non-Mutually Exclusive Events knowledge points

$$
LATEXBLOCK0
$$

Answer:

• (A) \(\frac{2}{9}\)
• (B) \(\frac{1}{2}\)
• (C) \(\frac{2}{3}\) (Correct answer)
• (D) \(\frac{5}{6}\)