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

Verified step by step guidance

1. Understand that each coin toss is an independent event with two possible outcomes: heads or tails, each with a probability of \(\frac{1}{2}\).
2. Since the coin is fair, the probability of getting heads on a single toss is \(\frac{1}{2}\).
3. To find the probability of getting all heads in six tosses, multiply the probability of heads for each toss together because the events are independent.
4. Express this multiplication as \(\left(\frac{1}{2}\right)^6\), which represents the probability of heads on toss 1 AND toss 2 AND ... AND toss 6.
5. This expression gives the probability of getting all heads in six tosses without calculating the final numerical value.

Key Concepts

Probability of a Single Event

Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. For a fair coin, the probability of getting heads in one toss is 1/2, since there are two equally likely outcomes.

Independent Events

Events are independent if the outcome of one does not affect the others. Tossing a coin multiple times are independent events, so the probability of multiple outcomes is the product of their individual probabilities.

Multiplication Rule for Independent Events

To find the probability of several independent events all occurring, multiply their individual probabilities. For six coin tosses all resulting in heads, multiply (1/2) six times, resulting in (1/2)^6.