Math Problem Statement

A coin is flipped three times, and the following list shows the possible outcomes.

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

What is the probability of getting at least one head?

Enter your answer as a reduced fraction, like this: 3/14

Solution

To find the probability of getting at least one head when flipping a coin three times, we can use the list of possible outcomes:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

There are a total of 8 possible outcomes, as there are 2 possibilities (H or T) for each flip, and 3 flips: 23=82^3 = 8.

Now, to find the probability of getting at least one head, we can first calculate the opposite (complementary) event, which is the probability of getting no heads at all, i.e., all tails.

The only outcome with no heads is:

  • TTT

So, there is 1 outcome where no heads appear. The probability of this happening is:

18\frac{1}{8}

Therefore, the probability of getting at least one head is the complement of this probability:

118=781 - \frac{1}{8} = \frac{7}{8}

Thus, the probability of getting at least one head is:

78\boxed{\frac{7}{8}}

Would you like any further details or clarification?


Here are five related questions for you:

  1. How do you calculate the probability of getting exactly two heads in three flips?
  2. What is the probability of getting two tails and one head in any order?
  3. How does the number of flips affect the total number of possible outcomes?
  4. What is the probability of getting no heads if you flip a coin four times?
  5. What are the odds of flipping exactly three heads in three coin flips?

Tip: Remember that the complement rule is a quick way to solve probability problems involving "at least one" or "at most one" type questions.

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Math Problem Analysis

Mathematical Concepts

Probability
Complementary Events

Formulas

Total possible outcomes = 2^n (where n is the number of flips)
Probability of an event = favorable outcomes / total outcomes
Complement Rule: P(at least one head) = 1 - P(no heads)

Theorems

Complementary Events

Suitable Grade Level

Grades 6-8