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

Verified step by step guidance

1. Understand that the problem involves finding the probability of a specific outcome when tossing a fair coin multiple times. Each toss is an independent event with two possible outcomes: heads or tails.
2. Recall that the probability of getting heads in a single toss of a fair coin is \( \frac{1}{2} \).
3. Since the coin tosses are independent, the probability of getting heads on all six tosses is the product of the probabilities of getting heads on each individual toss.
4. Express this as \( \left( \frac{1}{2} \right)^6 \), which means multiplying \( \frac{1}{2} \) by itself six times.
5. This expression represents the probability of getting all heads in six tosses, and you can leave it in this exponential form or calculate the numerical value if needed.

Key Concepts

Probability of Independent Events

When events are independent, the probability of all events occurring is the product of their individual probabilities. For example, each coin toss does not affect the others, so the combined probability is found by multiplying the probability of each toss outcome.

Probability of a Single Event

The probability of a single event is the ratio of favorable outcomes to total possible outcomes. For a fair coin, the probability of getting heads in one toss is 1/2, since there are two equally likely outcomes: heads or tails.

Multiplication Rule for Multiple Tosses

To find the probability of getting all heads in multiple tosses, multiply the probability of heads on each toss. For six tosses, this is (1/2) multiplied by itself six times, or (1/2)^6, representing the chance of heads occurring consecutively.