Flipping a Coin What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.

Verified step by step guidance

1. Identify the nature of the experiment: flipping a fair coin multiple times, where each flip is independent and has two possible outcomes (heads or tails) with equal probability of 0.5.
2. Recognize that the probability of getting heads on a single flip is \$0.5\( (or \)\frac{1}{2}$).
3. Since the flips are independent, the probability of getting heads on five consecutive flips is the product of the probabilities of each individual flip resulting in heads.
4. Write the probability of five heads in a row as \(\left(\frac{1}{2}\right)^5\) or \$0.5^5$.
5. Interpret this probability as the likelihood of this specific sequence (five heads in a row) occurring in one set of five flips, which is a relatively small chance given the exponential decrease with each additional required head.

Key Concepts

Probability of Independent Events

When events are independent, the probability of all occurring is the product of their individual probabilities. For coin flips, each flip does not affect the next, so the probability of multiple heads in a row is the product of the probability of heads on each flip.

Probability of a Single Event

The probability of a single event is the likelihood it will occur, expressed as a number between 0 and 1. For a fair coin, the probability of landing heads on one flip is 0.5, since there are two equally likely outcomes.

Interpreting Probability Values

Probability values indicate how likely an event is to happen. A probability close to 1 means the event is very likely, while a value near 0 means it is unlikely. Interpreting the probability of five heads in a row helps understand the rarity of this outcome.