Problem Description:
The image shows a spinner divided into 10 equal sections, each colored differently. The colors are as follows:
-
Blue: 3 sections
-
Red: 4 sections
-
Green: 3 sections
-
Yellow: 1 section
The task is to determine the probability of the spinner landing on a specific color when spun.
Solution:
#### Step 1: Understand the Total Number of Outcomes
The spinner is divided into 10 equal sections. Therefore, the total number of possible outcomes when the spinner is spun is:
\[
\text{Total outcomes} = 10
\]
#### Step 2: Determine the Number of Favorable Outcomes for Each Color
-
Blue: There are 3 sections colored blue.
-
Red: There are 4 sections colored red.
-
Green: There are 3 sections colored green.
-
Yellow: There is 1 section colored yellow.
#### Step 3: Calculate the Probability for Each Color
The probability \( P \) of the spinner landing on a specific color is given by the ratio of the number of favorable outcomes to the total number of outcomes. Mathematically:
\[
P(\text{Color}) = \frac{\text{Number of sections of that color}}{\text{Total number of sections}}
\]
-
Probability of landing on Blue:
\[
P(\text{Blue}) = \frac{3}{10}
\]
-
Probability of landing on Red:
\[
P(\text{Red}) = \frac{4}{10} = \frac{2}{5}
\]
-
Probability of landing on Green:
\[
P(\text{Green}) = \frac{3}{10}
\]
-
Probability of landing on Yellow:
\[
P(\text{Yellow}) = \frac{1}{10}
\]
#### Step 4: Verify the Probabilities
To ensure correctness, the sum of the probabilities of all possible outcomes should equal 1:
\[
P(\text{Blue}) + P(\text{Red}) + P(\text{Green}) + P(\text{Yellow}) = \frac{3}{10} + \frac{4}{10} + \frac{3}{10} + \frac{1}{10} = \frac{11}{10} = 1
\]
The probabilities are correct.
Final Answer:
The probabilities of the spinner landing on each color are:
\[
\boxed{\frac{3}{10} \text{ (Blue)}, \frac{2}{5} \text{ (Red)}, \frac{3}{10} \text{ (Green)}, \frac{1}{10} \text{ (Yellow)}}
\]
Parent Tip: Review the logic above to help your child master the concept of geometric probability spinner.