Say you have a coin and you flip in 3 times. What is the probability that it lands on heads all three times? What is the probability that is lands on tails at least once?

Let's address each part of your question step by step:

### 1. **Probability of landing on heads all three times:**

Each coin flip is an independent event, and the probability of landing on heads in a single flip is \( \frac{1}{2} \). 

For three flips, the probability of getting heads each time is:
\[
P(\text{HHH}) = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right) = \left( \frac{1}{2} \right)^3 = \frac{1}{8}
\]
So, the probability of landing on heads all three times is \( \frac{1}{8} \).

### 2. **Probability of landing on tails at least once:**

The easiest way to find this probability is to use the complement rule. First, find the probability that the coin **never lands on tails** (i.e., it lands on heads all three times), which we already calculated as \( \frac{1}{8} \).

The probability of landing on tails at least once is the complement of landing on heads all three times:
\[
P(\text{at least one tails}) = 1 - P(\text{HHH}) = 1 - \frac{1}{8} = \frac{7}{8}
\]
Thus, the probability of landing on tails at least once is \( \frac{7}{8} \).

### Summary:
1. Probability of landing on heads all three times = \( \frac{1}{8} \)
2. Probability of landing on tails at least once = \( \frac{7}{8} \)

Would you like more details or clarifications?

Here are some related questions:
1. What is the probability of getting exactly two heads in three flips?
2. How many total outcomes are possible with three coin flips?
3. What is the probability of getting at least two heads in three flips?
4. What is the probability of getting no heads in three flips?
5. How would the probability change if you flipped the coin four times?

**Tip:** Using the complement rule often simplifies finding probabilities of "at least one" events!

Say you have a coin and you flip it 3 times. What is the probability that it lands on heads all three times? What is the probability that it lands on tails at least once?

Discover how to calculate the probability of getting heads three times and the probability of landing on tails at least once in a series of three coin flips. This solution involves concepts like independent events and the complement rule, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation