Probability Of Note Selection Calculating The Chances

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Let's dive into the world of probability with a fun scenario involving notes in a box! Imagine you have a box filled with different denominations of notes: a GHe1 note, a GHe2 note, a GHe5 note, a GHe10 note, and a GHe20 note. Now, suppose someone randomly selects a note from this box. We're going to explore the probabilities associated with this selection, specifically focusing on two key questions:

  • What's the chance of picking the GHe10 note?
  • What's the likelihood of selecting a note with a value greater than a certain amount?

This exercise is a fantastic way to grasp the fundamentals of probability. So, let's break down the problem and solve it step by step.

a. Finding the Probability of Selecting the GHc10 Note

Okay, guys, let's tackle the first part of our probability puzzle. We want to figure out the probability of selecting the GHe10 note. Probability, at its core, is about understanding the likelihood of a specific event happening. In our case, the event is picking that particular GHe10 note.

To calculate this probability, we need two key pieces of information:

  1. The total number of possible outcomes: This is simply the total number of notes in the box. We have a GHe1, a GHe2, a GHe5, a GHe10, and a GHe20 note. So, there are 5 notes in total.
  2. The number of favorable outcomes: This is the number of ways we can achieve the event we're interested in – picking the GHe10 note. Since there's only one GHe10 note in the box, there's only 1 favorable outcome.

Now, we can use the basic probability formula:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

In our case, this translates to:

Probability (selecting GHe10) = 1 / 5

So, the probability of selecting the GHe10 note is 1 out of 5, or 1/5. To express this as a percentage, we can divide 1 by 5 and multiply by 100%:

(1 / 5) * 100% = 20%

Therefore, there's a 20% chance of randomly selecting the GHe10 note from the box. Not too shabby, right?

Key Takeaways for this part:

  • Probability is about the chance of an event occurring.
  • We calculate probability by dividing favorable outcomes by total possible outcomes.
  • In this case, the probability of selecting the GHe10 note is 1/5 or 20%.

b. Finding the Probability of Selecting a Note with a Denomination Greater Than a Certain Value

Now, let's crank up the complexity a notch! The second part of our problem asks us to find the probability of selecting a note with a denomination greater than a certain value. To make things concrete, let's say we want to find the probability of selecting a note with a value greater than GHe5. This adds a little twist to the problem, but don't worry, we can handle it!

Remember, the core principle of probability remains the same: we need to identify the total possible outcomes and the favorable outcomes. The total number of possible outcomes hasn't changed; we still have 5 notes in the box. But the favorable outcomes are different now. We're not just looking for one specific note; we're looking for any note with a value greater than GHe5.

Let's list out the notes we have:

  • GHe1
  • GHe2
  • GHe5
  • GHe10
  • GHe20

Which of these notes have a denomination greater than GHe5? Well, the GHe10 and the GHe20 certainly do! So, we have 2 favorable outcomes in this case.

Now we can plug these numbers into our probability formula:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability (selecting a note greater than GHe5) = 2 / 5

So, the probability of selecting a note with a denomination greater than GHe5 is 2 out of 5, or 2/5. Let's convert this to a percentage:

(2 / 5) * 100% = 40%

Therefore, there's a 40% chance of randomly selecting a note with a value greater than GHe5 from the box. Cool, huh?

Expanding the Concept: What if we wanted the probability of selecting a note greater than or equal to GHe5?

This is a slight but important variation. Now, the GHe5 note itself would also be considered a favorable outcome. In this case, we'd have 3 favorable outcomes (GHe5, GHe10, and GHe20). The probability would then be 3/5, or 60%.

Key Takeaways for this part:

  • We can calculate the probability of a range of outcomes (e.g., values greater than a certain amount).
  • Carefully identify all the favorable outcomes that meet the specified criteria.
  • The phrase "greater than or equal to" includes the specified value itself.

Conclusion: Probability Unlocked!

There you have it! We've successfully navigated the world of probability using our box of notes. We've learned how to calculate the probability of a specific event (selecting the GHe10 note) and the probability of a range of events (selecting a note with a value greater than GHe5). The key takeaway is that probability is all about understanding the relationship between favorable outcomes and total possible outcomes.

By breaking down the problem into smaller steps and carefully identifying the relevant information, we can tackle even more complex probability scenarios. So, next time you encounter a probability question, remember the principles we've discussed here, and you'll be well on your way to solving it!

Further Exploration:

To really solidify your understanding of probability, try these exercises:

  1. What is the probability of selecting a note with a denomination less than GHe10?
  2. What is the probability of selecting either the GHe1 note or the GHe20 note?
  3. Imagine we add another GHe10 note to the box. How does this change the probability of selecting a GHe10 note?

Keep practicing, and you'll become a probability pro in no time!