Question

A student observes the following spinner. What is the probability of obtaining the red colour.

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{5}{3}$
• D. $\frac{7}{3}$

Hint:

For spinner problems, the probability of landing on a specific color is the ratio of the angular measure (or area) of that color's sector(s) to the total angle ($360^\circ$) or total area of the spinner. Carefully interpret the visual divisions.

Answer 1

The Correct Option is B

Step 1: Analyze the spinner's divisions.
The spinner is a circle. Visually inspecting the spinner, we can deduce the proportions of the different colored regions. The circle appears to be divided in such a way that the top semi-circle is split into three approximately equal parts, and the bottom semi-circle is one large part.
Let the total area of the spinner be 1 unit.
The top half represents \( \frac{1}{2} \) of the total area.
The bottom half represents \( \frac{1}{2} \) of the total area.
In the top half:
One section is labeled "Blue".
Two sections are labeled "Red".
If these three sections in the top half are equal, then each of them occupies \( \frac{1}{3} \) of the top half's area.
Step 2: Calculate the area occupied by the red color.
Area of one small section in the top half = \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \) of the total spinner area.
Since there are two "Red" sections in the top half:
Total area of Red sections = \( 2 \times \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \) of the total spinner area.
Step 3: Calculate the probability of obtaining the red color.
The probability of obtaining the red color is the ratio of the area occupied by red to the total area of the spinner: \[ P(\text{Red}) = \frac{\text{Area of Red sections}}{\text{Total Area of Spinner}} = \frac{1}{3} \] Step 4: Final Answer.
The probability of obtaining the red color is \( \frac{1}{3} \). \[ (2) \quad \frac{1}{3} \]