Let's break down the problem step by step to find out how many times we would expect to roll a six on this biased dice.
1. Understanding the Probability:
- We are given that the probability of rolling a six on this biased dice is \(\frac{4}{5}\).
2. Total Number of Rolls:
- The dice is rolled 500 times.
3. Calculating the Expected Number of Sixes:
- The concept of expected value in probability helps us determine the average outcome over many trials. In this scenario, to find the expected number of sixes, we multiply the total number of rolls by the probability of rolling a six.
Therefore, the expected number of sixes (\(E\)) is calculated as:
[tex]\[
E = (\text{probability of getting a six}) \times (\text{number of rolls})
\][/tex]
Substituting the given values:
[tex]\[
E = \left(\frac{4}{5}\right) \times 500
\][/tex]
4. Multiplying to Find the Expected Value:
- First, we multiply \(\frac{4}{5}\) by 500.
- \(\frac{4}{5}\) is equivalent to 0.8.
- Therefore, the calculation becomes:
[tex]\[
0.8 \times 500 = 400
\][/tex]
So, the expected number of times a six would be rolled out of 500 trials is [tex]\(\boxed{400}\)[/tex].
