Question

if you roll a 6 - sided die 24,000 times, what is the best prediction possible for the number of times you will roll a four? times

Explanation:

Step1: Determine probability of rolling a four

A 6 - sided die has 6 possible outcomes. The probability of rolling a four, \( P(4) \), is the number of favorable outcomes (1, since there's one face with 4) divided by the total number of outcomes (6). So \( P(4)=\frac{1}{6} \).

Step2: Calculate expected number of fours

To find the expected number of times we roll a four in \( n = 24000 \) rolls, we use the formula \( \text{Expected value}=n\times P(4) \). Substituting \( n = 24000 \) and \( P(4)=\frac{1}{6} \), we get \( 24000\times\frac{1}{6} \).
Calculating \( 24000\div6 = 4000 \).

Answer:

4000