Question
Predict the number of outcomes for the given number of rolls:
Outcome: even number
Number of rolls: 50
Outcome: even number
Number of rolls: 50
Answers
GPT-4o mini
When rolling a fair six-sided die, there are three even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number on a single roll is:
\[
P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
If you are rolling the die 50 times, you are essentially conducting 50 independent experiments (the rolls), each with a \( \frac{1}{2} \) chance of being an even number.
The expected number of even outcomes in 50 rolls can be calculated as:
\[
E(\text{even outcomes}) = \text{Number of rolls} \times P(\text{even}) = 50 \times \frac{1}{2} = 25
\]
So, you can expect, on average, to roll an even number approximately 25 times out of 50 rolls.
If you are asking for the total number of possible outcomes (not the expected even outcomes), each roll has 6 outcomes, and for 50 rolls, the total number of possible combinations of outcomes is:
\[
6^{50}
\]
However, if you're looking specifically for just rolling an even number versus rolling an odd number, the question centers around the expected outcome of 25 even results in 50 rolls.
In summary, if asking about the expected number of even outcomes over 50 rolls, the answer is 25. If asking about combinations of outcomes possible, then it's \(6^{50}\).
\[
P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2}
\]
If you are rolling the die 50 times, you are essentially conducting 50 independent experiments (the rolls), each with a \( \frac{1}{2} \) chance of being an even number.
The expected number of even outcomes in 50 rolls can be calculated as:
\[
E(\text{even outcomes}) = \text{Number of rolls} \times P(\text{even}) = 50 \times \frac{1}{2} = 25
\]
So, you can expect, on average, to roll an even number approximately 25 times out of 50 rolls.
If you are asking for the total number of possible outcomes (not the expected even outcomes), each roll has 6 outcomes, and for 50 rolls, the total number of possible combinations of outcomes is:
\[
6^{50}
\]
However, if you're looking specifically for just rolling an even number versus rolling an odd number, the question centers around the expected outcome of 25 even results in 50 rolls.
In summary, if asking about the expected number of even outcomes over 50 rolls, the answer is 25. If asking about combinations of outcomes possible, then it's \(6^{50}\).