What is the probability of flipping 3 heads in a row?
Understand the Problem
The question is asking for the likelihood of obtaining three heads in a row when flipping a fair coin. To solve this, we would consider the probability of getting heads on each individual flip and multiply those probabilities together since each flip is independent.
Answer
The probability of getting three heads in a row is $\frac{1}{8}$.
Answer for screen readers
The probability of getting three heads in a row when flipping a fair coin is $\frac{1}{8}$.
Steps to Solve
- Determine the probability of getting heads in one flip
For a fair coin, the probability of getting heads in one flip is
$$ P(\text{heads}) = \frac{1}{2} $$
- Calculate the probability for three independent flips
Since each flip is independent, the probability of getting heads three times in a row can be found by multiplying the probability of getting heads in each individual flip:
$$ P(\text{3 heads}) = P(\text{heads}) \times P(\text{heads}) \times P(\text{heads}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) $$
- Compute the final probability
Now, we can simplify the expression from the previous step:
$$ P(\text{3 heads}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} $$
The probability of getting three heads in a row when flipping a fair coin is $\frac{1}{8}$.
More Information
This means that out of every 8 sets of three coin flips, on average, you would expect to get three heads in a row once. Coin flips are classic examples of independent events in probability theory.
Tips
- Misunderstanding independence: It's crucial to remember that each coin flip does not affect the outcomes of other flips.
- Incorrectly summing probabilities: Some might mistakenly add the probabilities instead of multiplying them since getting multiple events in series requires multiplication.
