Answered

During an experiment, Juan rolled a six-sided number cube 18 times. The number two occurred four times. Juan claimed the experimental probability of rolling a two was approximately [tex]\frac{1}{9}[/tex]. Which of the following is true about Juan's claim?

A. Juan's claim is incorrect. The correct experimental probability is [tex]\frac{2}{9}[/tex].
B. Juan's claim is incorrect. The correct experimental probability is [tex]\frac{1}{3}[/tex].
C. Juan's claim is incorrect. The correct experimental probability is [tex]\frac{4}{9}[/tex].
D. Juan's claim is correct.



Answer :

GinnyAnswer
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].

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