If you toss a fair coin six times, what is the probability of getting all heads?

Verified step by step guidance

1. Step 1: Understand that a fair coin has two possible outcomes for each toss: heads (H) or tails (T).
2. Step 2: Recognize that the probability of getting heads on a single toss of a fair coin is \( \frac{1}{2} \).
3. Step 3: Since the coin is tossed six times, and each toss is independent, the probability of getting heads on all six tosses is the product of the probabilities of getting heads on each individual toss.
4. Step 4: Calculate the probability of getting heads on all six tosses by raising the probability of a single head to the power of the number of tosses: \( \left( \frac{1}{2} \right)^6 \).
5. Step 5: Simplify the expression \( \left( \frac{1}{2} \right)^6 \) to find the probability of getting all heads in six tosses.

Key Concepts

Probability Basics

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. In the context of a fair coin toss, the probability of getting heads in a single toss is 0.5, as there are two equally likely outcomes: heads or tails.

Independent Events

Independent events are those whose outcomes do not affect each other. In this case, each coin toss is independent; the result of one toss does not influence the results of the others. Therefore, the probability of multiple independent events occurring together is the product of their individual probabilities.

Calculating Compound Probability

To find the probability of multiple independent events all occurring, you multiply their individual probabilities. For example, the probability of getting heads six times in a row is calculated as (0.5)^6, which represents the probability of heads for each of the six tosses multiplied together.