The Formula for Probability

Oct 13, 2025 by wbrum.org 86 views

**What is the Probability of Drawing a Green Scarf Out of a Drawer?** ===========================================================

Introduction

Probability is a measure of the likelihood of an event occurring. In this article, we will explore the concept of probability and apply it to a real-world scenario. We will calculate the probability of drawing a green scarf out of a drawer containing 6 green, 8 blue, and 4 black scarves.

Understanding Probability

Probability is a number between 0 and 1 that represents the likelihood of an event occurring. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.

The Formula for Probability

The formula for probability is:

P(E) = Number of favorable outcomes / Total number of possible outcomes

Where P(E) is the probability of the event, and E is the event itself.

Calculating the Probability of Drawing a Green Scarf

Let's apply the formula for probability to our scenario. We want to calculate the probability of drawing a green scarf out of a drawer containing 6 green, 8 blue, and 4 black scarves.

Step 1: Identify the Number of Favorable Outcomes

The number of favorable outcomes is the number of green scarves in the drawer, which is 6.

Step 2: Identify the Total Number of Possible Outcomes

The total number of possible outcomes is the total number of scarves in the drawer, which is 6 + 8 + 4 = 18.

Step 3: Calculate the Probability

Now we can calculate the probability of drawing a green scarf using the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 6 / 18 P(E) = 1/3 P(E) = 0.33

Conclusion

The probability of drawing a green scarf out of a drawer containing 6 green, 8 blue, and 4 black scarves is 1/3 or 0.33. This means that if you were to draw a scarf from the drawer at random, there is a 33.33% chance that it would be green.

Frequently Asked Questions

Q: What is the probability of drawing a blue scarf?

A: To calculate the probability of drawing a blue scarf, we need to identify the number of blue scarves (8) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 8 / 18 P(E) = 4/9 P(E) = 0.44

So the probability of drawing a blue scarf is 4/9 or 0.44.

Q: What is the probability of drawing a black scarf?

A: To calculate the probability of drawing a black scarf, we need to identify the number of black scarves (4) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 4 / 18 P(E) = 2/9 P(E) = 0.22

So the probability of drawing a black scarf is 2/9 or 0.22.

Q: What is the probability of drawing a non-green scarf?

A: To calculate the probability of drawing a non-green scarf, we need to identify the number of non-green scarves (8 blue + 4 black = 12) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 12 / 18 P(E) = 2/3 P(E) = 0.67

So the probability of drawing a non-green scarf is 2/3 or 0.67.

Q: What is the probability of drawing a green or blue scarf?

A: To calculate the probability of drawing a green or blue scarf, we need to identify the number of green scarves (6) and blue scarves (8) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 6 + 8 / 18 P(E) = 14 / 18 P(E) = 7/9 P(E) = 0.78

So the probability of drawing a green or blue scarf is 7/9 or 0.78.

Q: What is the probability of drawing a green or black scarf?

A: To calculate the probability of drawing a green or black scarf, we need to identify the number of green scarves (6) and black scarves (4) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 6 + 4 / 18 P(E) = 10 / 18 P(E) = 5/9 P(E) = 0.56

So the probability of drawing a green or black scarf is 5/9 or 0.56.

Q: What is the probability of drawing a green, blue, or black scarf?

A: To calculate the probability of drawing a green, blue, or black scarf, we need to identify the number of green scarves (6), blue scarves (8), and black scarves (4) and the total number of possible outcomes (18). Then we can use the formula:

P(E) = Number of favorable outcomes / Total number of possible outcomes P(E) = 6 + 8 + 4 / 18 P(E) = 18 / 18 P(E) = 1 P(E) = 1.00

So the probability of drawing a green, blue, or black scarf is 1 or 100%.

Q: What is the probability of drawing a non-green, non-blue, or non-black scarf?

A: Since there are only three colors of scarves (green, blue, and black), the probability of drawing a non-green, non-blue, or non-black scarf is 0.