Question

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 (\frac{1}{9}). which of the following is true about juan’s claim?

• juan’s claim is incorrect. the correct experimental probability is (\frac{2}{9})
• juan’s claim is incorrect. the correct experimental probability is (\frac{1}{3})
• juan’s claim is incorrect. the correct experimental probability is (\frac{4}{9})
• juan’s claim is correct

Explanation:

Step1: Recall experimental probability formula

Experimental probability = $\frac{\text{Number of successful trials}}{\text{Total number of trials}}$

Step2: Identify values

Successful trials (rolling a two) = 4, Total trials = 18

Step3: Calculate experimental probability

Experimental probability = $\frac{4}{18}=\frac{2}{9}$

Step4: Compare with Juan's claim

Juan claimed it was $\frac{1}{9}$. Since $\frac{2}{9}
eq\frac{1}{9}$, his claim is incorrect, and the correct probability is $\frac{2}{9}$.

Answer:

Juan's claim is incorrect. The correct experimental probability is $\frac{4}{18}=\frac{2}{9}$ (Wait, no, wait: Wait, the number of trials is 18, and the number of times two occurred is 4. So experimental probability is $\frac{4}{18}=\frac{2}{9}$? Wait, no, the problem says "Juan claimed the experimental probability of rolling a two was approximately $\frac{1}{9}$". Wait, let's recalculate:

Experimental probability = number of successful trials / total number of trials. So successful trials (rolling a two) is 4, total trials is 18. So experimental probability is $\frac{4}{18}=\frac{2}{9}$? Wait, no, 4 divided by 18 is $\frac{2}{9}$? Wait, 4/18 simplifies to 2/9? Wait, 4 ÷ 2 = 2, 18 ÷ 2 = 9. Yes. But wait, the options: Let's check the options again. Wait, the options are:

1. Juan’s claim is incorrect. The correct experimental probability is $\frac{2}{9}$.

1. Juan’s claim is incorrect. The correct experimental probability is $\frac{1}{3}$.

1. Juan’s claim is incorrect. The correct experimental probability is $\frac{4}{9}$.

1. Juan’s claim is correct.

Wait, Juan claimed the experimental probability was approximately $\frac{1}{9}$. Let's calculate the actual experimental probability: number of times two occurred is 4, total rolls is 18. So experimental probability is $\frac{4}{18}=\frac{2}{9}\approx0.222$, and $\frac{1}{9}\approx0.111$. So Juan's claim is incorrect, and the correct experimental probability is $\frac{4}{18}=\frac{2}{9}$? Wait, no, 4/18 is 2/9? Wait, 4 divided by 18: 4 ÷ 18 = 0.222..., and 2/9 is also 0.222..., yes. Wait, but let's check the options. The first option says "Juan’s claim is incorrect. The correct experimental probability is $\frac{2}{9}$"? Wait, no, the user's image: Let me re-express the options as per the image (since the image has some text):

Looking at the image, the options are:

• Juan’s claim is incorrect. The correct experimental probability is $\frac{2}{9}$.

• Juan’s claim is incorrect. The correct experimental probability is $\frac{1}{3}$.

• Juan’s claim is incorrect. The correct experimental probability is $\frac{4}{9}$.

• Juan’s claim is correct.

So let's compute the experimental probability:

Experimental probability = (number of times two occurred) / (total number of rolls) = 4 / 18 = 2 / 9 ≈ 0.222.

Juan claimed it was approximately 1/9 ≈ 0.111. So his claim is incorrect, and the correct experimental probability is 2/9. So the first option is correct.