Let's break down the problem step by step:
1. Calculate the Experimental Probability:
- The number two appeared 4 times out of 18 rolls.
- The experimental probability [tex]\( P(E) \)[/tex] of rolling a two can be calculated using the formula:
[tex]\[
P(E) = \frac{\text{Number of successful outcomes}}{\text{Total number of trials}}
\][/tex]
- Substituting the given values:
[tex]\[
P(E) = \frac{4}{18}
\][/tex]
- Simplifying the fraction:
[tex]\[
P(E) = \frac{2}{9} \approx 0.2222
\][/tex]
2. Juan's Claim:
- Juan claimed the experimental probability is approximately [tex]\( \frac{1}{9} \)[/tex].
- Let's convert [tex]\( \frac{1}{9} \)[/tex] to a decimal to compare:
[tex]\[
\frac{1}{9} \approx 0.1111
\][/tex]
3. Comparison:
- Comparing the two probabilities:
- Experimental Probability: [tex]\( \frac{2}{9} \approx 0.2222 \)[/tex]
- Juan's Claim: [tex]\( \frac{1}{9} \approx 0.1111 \)[/tex]
4. Conclusion:
- We see that [tex]\( 0.2222 \neq 0.1111 \)[/tex].
- Therefore, Juan's claim is incorrect because the correct experimental probability is [tex]\( \frac{2}{9} \)[/tex].
The correct statement is:
- Juan's claim is incorrect. The correct experimental probability is [tex]\( \frac{2}{9} \)[/tex].
