https://file.aiquickdraw.com/mathbot/file/1726754708184kc9c5f1c.jpg

To solve this problem, we need to determine the probability that a randomly selected student **does not play Football**.

### Step 1: Find the total number of students playing Football.

The Football circle in the Venn diagram contains the following values:
- 4 (only Football),
- 14 (Football and Hockey),
- 31 (Football, Hockey, and Rugby),
- 17 (Football and Rugby).

So, the total number of students playing Football is:
\[
4 + 14 + 31 + 17 = 66.
\]

### Step 2: Find the total number of students not playing Football.
The total number of students is given as 80. Therefore, the number of students **not** playing Football is:
\[
80 - 66 = 14.
\]

### Step 3: Calculate the probability.
The probability of selecting a student who does **not** play Football is the ratio of students who do not play Football to the total number of students:
\[
\frac{14}{80} = \frac{7}{40}.
\]

So, the probability is **\(\frac{7}{40}\)** or approximately **0.175**.

Do you want further details or clarifications on this? 

Here are five relative questions to expand on the concept:
1. How do you calculate probabilities for students playing multiple sports?
2. What is the probability of picking a student who plays only Rugby?
3. How would the probability change if 10 more students were added, none of whom play Football?
4. How can the complement rule be used in this type of probability problem?
5. Can you calculate the probability of selecting a student who plays at least two sports?

**Tip:** When dealing with probabilities, always double-check the total count and ensure you're considering overlaps carefully, especially with Venn diagrams.

If a student is picked at random, what is the probability that they don’t play Football?

Learn how to calculate the probability that a student does not play football, given a Venn diagram. We explore the complement rule in probability and apply it to a real-world scenario involving students who play multiple sports. This guide is suitable for Grade 8-10 students studying probability and set theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation