a pathological video game user(PVGU) is à video game user averages 31 or more hours a week of of gameplay. ### Understanding Pathological Video Game Use Among YouthsA pathological video game user (PVGU) is defined as a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs.### Probability Calculation ExampleSuppose five youths in grades 3–8 are randomly selected. Let $ X $ represent the number of youths who are PVGUs in this sample. Here are the given and calculated values for the probability distribution:1. **Sample size** $(n)$: \[ n = 7 \]2. **Probability of a child being a PVGU** $(p)$: \[ p = 0.09 \]3. **Probability of a child not being a PVGU** $(1 - p)$: \[ 1 - p = 0.91 \]### Probability Distribution TableThe table below presents the probability distribution for the random variable $X$, representing the number of PVGUs among the sampled youths. The values are calculated and rounded to four decimal places.| $X = x$ | $P(X = x)$ ||-----------|--------------|| 0 | 0.5170 || 1 | 0.3580 |### Explanation of CalculationTo compute the probabilities for each possible number of PVGUs in the sample, we use the binomial probability formula:\[P(X = x) = \binom{n}{x} p^x (1 - p)^{n - x}\]Where:- $ \binom{n}{x} $ is the binomial coefficient- $ p $ is the probability of success (being a PVGU)- $ (1 - p) $ is the probability of failure (not being a PVGU)- $ n $ is the number of trials (youths sampled)- $ x $ is the number of successes (number of PVGUs)### ConclusionAnalyzing

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Description: a pathological video game user(PVGU) is à video game user averages 31 or more hours a week of of gameplay. ### Understanding Pathological Video Game Use Among YouthsA pathological video game user (PVGU) is defined as a video game user that averages

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a pathological video game user(PVGU) is à video game user averages 31 or more hours a week of of gameplay.

### Understanding Pathological Video Game Use Among Youths

A pathological video game user (PVGU) is defined as a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs.

### Probability Calculation Example

Suppose five youths in grades 3–8 are randomly selected. Let $ X $ represent the number of youths who are PVGUs in this sample. Here are the given and calculated values for the probability distribution:

1. **Sample size** $(n)$:
\[
n = 7
\]

2. **Probability of a child being a PVGU** $(p)$:
\[
p = 0.09
\]

3. **Probability of a child not being a PVGU** $(1 - p)$:
\[
1 - p = 0.91
\]

### Probability Distribution Table

The table below presents the probability distribution for the random variable $X$, representing the number of PVGUs among the sampled youths. The values are calculated and rounded to four decimal places.

| $X = x$ | $P(X = x)$ |
|-----------|--------------|
| 0 | 0.5170 |
| 1 | 0.3580 |

### Explanation of Calculation

To compute the probabilities for each possible number of PVGUs in the sample, we use the binomial probability formula:

\[
P(X = x) = \binom{n}{x} p^x (1 - p)^{n - x}
\]

Where:
- $ \binom{n}{x} $ is the binomial coefficient
- $ p $ is the probability of success (being a PVGU)
- $ (1 - p) $ is the probability of failure (not being a PVGU)
- $ n $ is the number of trials (youths sampled)
- $ x $ is the number of successes (number of PVGUs)

### Conclusion

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A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs.

Calculate the probability that EXACTLY three youths are PVGUs

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