Math Problem Statement

If a fair coin is used, what is the probability that one toss will result in heads or tails? Explain why your answer makes sense.

Solution

The question asks about the probability of a fair coin toss resulting in either heads or tails.

For a fair coin, there are two possible outcomes: heads or tails. Since the coin is fair, the probability of each outcome is the same.

  • Probability of heads = 1/2
  • Probability of tails = 1/2

The total probability of the coin landing either heads or tails is the sum of the two probabilities: P(Heads or Tails)=12+12=1P(\text{Heads or Tails}) = \frac{1}{2} + \frac{1}{2} = 1

This makes sense because these are the only two possible outcomes when tossing a fair coin, and one of them must occur.

Would you like more details on probability or have any other questions? Here's a quick expansion of the topic:

  1. What is the definition of a probability event?
  2. How do you calculate the probability of multiple events happening?
  3. What is the probability of an impossible event?
  4. How does the fairness of a coin affect its probability?
  5. What is the probability of getting heads in 3 tosses of a fair coin?

Tip: Remember, the total probability for all possible outcomes in a sample space always adds up to 1!

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Math Problem Analysis

Mathematical Concepts

Probability
Random Events

Formulas

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

Theorems

Law of Total Probability

Suitable Grade Level

Grades 6-8