Graduate Management Admission Test (GMAT) Practice Test

How is the probability of a specific combination calculated when flipping coins?

1. Sum of all outcomes

2. Probability of single outcomes multiplied by number of ways

3. Factorial of total flips divided by specific outcomes

4. Probability divided by total arrangements

The correct answer is: Probability of single outcomes multiplied by number of ways

The correct option highlights a fundamental principle in probability theory, particularly when dealing with independent events like flipping coins. When considering the probability of a specific combination occurring during a series of coin flips, you first determine the probability of getting the desired outcome for each individual flip. For a fair coin, the probability of getting either heads or tails in a single flip is \( \frac{1}{2} \). Once the probability of a single outcome is established, it needs to be multiplied by the number of ways that this specific combination can occur across all the flips. This is important because multiple arrangements of flips can lead to the same combination of outcomes. For instance, if you are interested in the probability of getting 2 heads and 3 tails in 5 flips, not only do you calculate the probability of getting heads and tails individually, but you must also account for the different sequences in which these can occur. This is where the combination factor comes into play, allowing you to represent all the ways to arrange heads and tails within the total number of flips. This understanding is essential when analyzing more complex scenarios, as it allows for accurate calculations of probabilities concerning combinations or patterns of outcomes in experiments involving chance. In summary, the probability of a specific combination is effectively