Probability of Drawing a Red Sock

Oct 13, 2025 by vinooalluri.com 50 views

Lesson 1 Extra Practice: Probability of Simple Events

Understanding Probability

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this lesson, we will explore the concept of probability and how to calculate it for simple events.

The Problem

Two socks are drawn from a drawer that contains one red sock, three blue socks, two black socks, and two green socks. Once a sock is selected, it is not replaced. We need to find the probability of drawing each type of sock.

Step 1: Define the Sample Space

The sample space is the set of all possible outcomes. In this case, the sample space consists of the following outcomes:

Red sock (R)
Blue sock (B)
Black sock (K)
Green sock (G)

There are a total of 8 socks in the drawer, so the sample space has 8 elements.

Step 2: Define the Event

The event is the specific outcome we are interested in. In this case, we want to find the probability of drawing each type of sock.

Step 3: Count the Number of Favorable Outcomes

The number of favorable outcomes is the number of outcomes that satisfy the event. For example, if we want to find the probability of drawing a red sock, the number of favorable outcomes is 1 (since there is only one red sock in the drawer).

Step 4: Calculate the Probability

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the total number of outcomes is 8 (since there are 8 socks in the drawer).

Calculating the Probability of Drawing Each Type of Sock

Let's calculate the probability of drawing each type of sock:

Probability of Drawing a Red Sock

The number of favorable outcomes is 1 (since there is only one red sock in the drawer). The total number of outcomes is 8. Therefore, the probability of drawing a red sock is:

1/8 = 0.125

Probability of Drawing a Blue Sock

The number of favorable outcomes is 3 (since there are three blue socks in the drawer). The total number of outcomes is 8. Therefore, the probability of drawing a blue sock is:

3/8 = 0.375

Probability of Drawing a Black Sock

The number of favorable outcomes is 2 (since there are two black socks in the drawer). The total number of outcomes is 8. Therefore, the probability of drawing a black sock is:

2/8 = 0.25

Probability of Drawing a Green Sock

The number of favorable outcomes is 2 (since there are two green socks in the drawer). The total number of outcomes is 8. Therefore, the probability of drawing a green sock is:

2/8 = 0.25

Conclusion

In this lesson, we learned how to calculate the probability of simple events. We used the formula P(event) = Number of favorable outcomes / Total number of outcomes to calculate the probability of drawing each type of sock. We found that the probability of drawing a red sock is 0.125, the probability of drawing a blue sock is 0.375, the probability of drawing a black sock is 0.25, and the probability of drawing a green sock is 0.25.

Practice Problems

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a red marble?
A box contains 2 red balls, 4 blue balls, and 1 green ball. What is the probability of drawing a blue ball?
A deck of cards contains 52 cards, with 4 suits (hearts, diamonds, clubs, and spades). What is the probability of drawing a heart?

Answer Key

5/10 = 0.5
4/7
13/52 = 1/4

Discussion Questions

What is the difference between a simple event and a compound event?
How do you calculate the probability of a compound event?
What is the relationship between probability and chance?

Additional Resources

Khan Academy: Probability
Math Is Fun: Probability
Wolfram MathWorld: Probability
Lesson 1 Extra Practice: Probability of Simple Events - Q&A

Understanding Probability

Q&A

Q: What is the difference between a simple event and a compound event?

A: A simple event is an event that can occur in only one way, while a compound event is an event that can occur in multiple ways.

Q: How do you calculate the probability of a simple event?

A: To calculate the probability of a simple event, you need to divide the number of favorable outcomes by the total number of outcomes.

Q: What is the formula for calculating the probability of a simple event?

A: The formula for calculating the probability of a simple event is:

P(event) = Number of favorable outcomes / Total number of outcomes

Q: What is the probability of drawing a red sock from a drawer that contains 1 red sock, 3 blue socks, 2 black socks, and 2 green socks?

A: The probability of drawing a red sock is 1/8, since there is only 1 red sock in the drawer and a total of 8 socks.

Q: What is the probability of drawing a blue sock from a drawer that contains 1 red sock, 3 blue socks, 2 black socks, and 2 green socks?

A: The probability of drawing a blue sock is 3/8, since there are 3 blue socks in the drawer and a total of 8 socks.

Q: What is the probability of drawing a black sock from a drawer that contains 1 red sock, 3 blue socks, 2 black socks, and 2 green socks?

A: The probability of drawing a black sock is 2/8, since there are 2 black socks in the drawer and a total of 8 socks.

Q: What is the probability of drawing a green sock from a drawer that contains 1 red sock, 3 blue socks, 2 black socks, and 2 green socks?

A: The probability of drawing a green sock is 2/8, since there are 2 green socks in the drawer and a total of 8 socks.

Q: What is the relationship between probability and chance?

A: Probability and chance are related, but they are not the same thing. Probability is a measure of the likelihood of an event occurring, while chance is the degree of uncertainty or unpredictability of an event.

Q: How do you calculate the probability of a compound event?

A: To calculate the probability of a compound event, you need to use the formula:

P(event) = P(event1) + P(event2) + ... + P(eventn)

where P(event1), P(event2), ..., P(eventn) are the probabilities of each individual event.

Q: What is the difference between an independent event and a dependent event?

A: An independent event is an event that can occur independently of other events, while a dependent event is an event that is affected by other events.

Q: How do you calculate the probability of an independent event?

A: To calculate the probability of an independent event, you need to multiply the probabilities of each individual event.

Q: What is the formula for calculating the probability of an independent event?

A: The formula for calculating the probability of an independent event is:

P(event) = P(event1) × P(event2) × ... × P(eventn)