Desmond is rolling a standard six-sided die 72 times. Approximately how many times would Desmond roll a 4 and why?
Understand the Problem
The question is asking for an estimation of how many times the number 4 will appear when rolling a six-sided die 72 times, based on probability.
Answer
12
Answer for screen readers
The expected number of times the number 4 will appear when rolling a six-sided die 72 times is 12.
Steps to Solve
-
Identify the probability of rolling a 4 The probability of rolling a particular number (in this case, a 4) on a six-sided die is given by: $$ P(rolling\ 4) = \frac{1}{6} $$
-
Determine the total number of rolls We are rolling the die 72 times, so we can use this in our calculations.
-
Calculate the expected number of times to roll a 4 To find the expected number of times to roll a 4, multiply the probability of rolling a 4 by the total number of rolls (72): $$ Expected\ rolls\ of\ 4 = P(rolling\ 4) \times Total\ rolls $$ $$ Expected\ rolls\ of\ 4 = \frac{1}{6} \times 72 $$
-
Perform the calculation Now, perform the multiplication: $$ Expected\ rolls\ of\ 4 = \frac{72}{6} = 12 $$
The expected number of times the number 4 will appear when rolling a six-sided die 72 times is 12.
More Information
This calculation is based on the principle of probability, where each face of the die has an equal chance of appearing. Since there are 6 faces, the chance of rolling a 4 is $\frac{1}{6}$. Therefore, in 72 rolls, the average or expected occurrence would be 12 times.
Tips
- Confusing probability and expected value: It's important to remember that the expected value isn't a guarantee but rather an average over many trials.
- Using wrong total rolls: Make sure to use the correct number of rolls, which is given in the problem.
AI-generated content may contain errors. Please verify critical information
