Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The higher the probability, the more likely the event is to occur. ...
Calculating Probability
In this scenario, we have a collection of items with different colors: 5 green, 6 yellow, 8 blue, and 7 brown. To determine the probability of choosing a blue item, we need to follow these steps:
- Identify the favorable outcome: We want to choose a blue item.
- Count the total number of favorable outcomes: There are 8 blue items.
- Count the total number of possible outcomes: There are 5 + 6 + 8 + 7 = 26 items in total.
- Calculate the probability: Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Applying the Formula
In our case, the probability of choosing a blue item is:
Probability (Blue) = 8 / 26 = 4/13
Simplifying the Answer
The probability 4/13 is already in its simplest form. It represents the probability of choosing a blue item, which means there are 4 chances out of 13 that you will select a blue item.
Key Concepts
Here are some essential concepts related to probability that are relevant to this problem:
- Sample space: The set of all possible outcomes. In this case, the sample space is the collection of all the items (green, yellow, blue, and brown).
- Event: A specific outcome or set of outcomes. Choosing a blue item is our event of interest.
- Favorable outcome: An outcome that fulfills the desired condition. Choosing a blue item is our favorable outcome.
Conclusion
The probability of choosing a blue item from a collection of 5 green, 6 yellow, 8 blue, and 7 brown items is 4/13. This means there is a 4 out of 13 chance that you will select a blue item. Understanding probability is crucial in various fields, including statistics, finance, and decision-making. It allows us to quantify uncertainty and make informed predictions about future events.