Over the past weekend, Antioch High School (AHS) competed in a swim meet where 20 athletes competed for individual events to earn a combined team total of 46 points. A first-place finish earns 5 points, a second-place finish earns 3 points, and a third-place finish earns 1 point. AHS had a strong third-place showing, with as many third-place finishers as first- and second-place finishers combined. How many athletes finished in the first place?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Over the past weekend, Antioch High School (AHS) competed in a swim meet where 20 athletes competed for individual events to earn a combined team total of 46 points. A first-place finish earns 5 points, a second-place finish earns 3 points, and a third-place finish earns 1 point. AHS had a strong third-place showing, with as many third-place finishers as first- and second-place finishers combined.
How many athletes finished in the first place?
Given that,
Antioch High School (AHS) competed in a swim meet where 20 athletes competed for individual events to earn a combined team total of 46 points.
Thus total points are 46.
A first-place finish earns 5 points, a second-place finish earns 3 points, and a third-place finish earns 1 point. AHS had a strong third-place showing, with as many third-place finishers as first- and second-place finishers combined.
Let the number of first-place finishers is x and the number of second-place finishers is y, the number of third-place finishers is z.
The total number of athletes is 20.
Hence x + y +z = 20
A first-place finish earns 5 points, a second-place finish earns 3 points, and a third-place finish earns 1 point.
Total points are 46
Thus. 5x + 3 y +z = 46
AHS had a strong third-place showing, with as many third-place finishers as first- and second-place finishers combined.
Thus, z = x+y
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
