An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Calculate the total number of series: N = 20 + 23 + 25 + 31 = 99 .
Calculate the probability for 4 games: P ( X = 4 ) = 99 20 ​ ≈ 0.2020 .
Calculate the probability for 5 games: P ( X = 5 ) = 99 23 ​ ≈ 0.2323 .
Calculate the probability for 6 games: P ( X = 6 ) = 99 25 ​ ≈ 0.2525 .
Calculate the probability for 7 games: P ( X = 7 ) = 99 31 ​ ≈ 0.3131 .
The discrete probability distribution is: P ( X = 4 ) = 0.2020 , P ( X = 5 ) = 0.2323 , P ( X = 6 ) = 0.2525 , P ( X = 7 ) = 0.3131 .

Explanation

Understand the problem and provided data We are given the frequency of games played in a tournament from 1923 to 2022. Our goal is to construct a discrete probability distribution for the random variable X , which represents the number of games played. The probability P ( x ) for each value of x (number of games) is calculated as P ( x ) = N f ​ , where f is the frequency of that number of games and N is the total number of games.

Calculate the total number of series First, we need to calculate the total number of series, N , by summing the frequencies for each number of games: N = 20 + 23 + 25 + 31 = 99 So, there are a total of 99 series.

Calculate the probability for each number of games Now, we calculate the probability for each number of games by dividing its frequency by the total number of series:


For 4 games: P ( X = 4 ) = 99 20 ​ ≈ 0.2020
For 5 games: P ( X = 5 ) = 99 23 ​ ≈ 0.2323
For 6 games: P ( X = 6 ) = 99 25 ​ ≈ 0.2525
For 7 games: P ( X = 7 ) = 99 31 ​ ≈ 0.3131

Construct the probability distribution table We have calculated the probabilities for each possible number of games played. Now, we can fill in the table with these probabilities, rounded to four decimal places:




x (games played)
P ( x )



4
0.2020


5
0.2323


6
0.2525


7
0.3131


Examples
Discrete probability distributions are useful in many real-world scenarios. For example, in sports analytics, we can use them to model the number of goals scored in a soccer match, the number of runs in a baseball game, or, as in this case, the number of games in a tournament series. By understanding the probabilities associated with different outcomes, analysts can make predictions, assess risks, and develop strategies. This helps in making informed decisions related to team management, player selection, and betting strategies.

Answered by GinnyAnswer | 2025-07-05

In this problem, the total charge delivered by the electric device is 450 C , which corresponds to roughly 2.81 × 1 0 21 electrons flowing through the device in 30 seconds. The calculations involve using the relationship between current, charge, and the elementary charge of an electron. Thus, this illustrates how we can calculate the number of electrons based on current and duration.
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Answered by Anonymous | 2025-07-06