Probability Of Selecting A Month Starting With J Or M

by Scholario Team 54 views

Hey there, math enthusiasts! Today, we're diving into a probability question that's both fun and engaging. We're going to tackle a problem that involves the months of the year and the likelihood of picking one that starts with a specific letter. So, grab your thinking caps, and let's get started!

The Probability Problem

Here's the question we're going to solve:

A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

A. $\frac{5}{24}$

B. $\frac{1}{6}$ C. $\frac{1}{4}$ D. $\frac{1}{12}$

Before we jump into the solution, let's break down what this question is asking. We need to figure out the chance of randomly selecting a month from the year that begins with either the letter "J" or the letter "M." Probability, at its core, is about understanding the likelihood of an event occurring. In this case, our event is picking a month that meets our criteria.

Understanding Probability Basics

To solve this, let's quickly recap the basics of probability. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Think of it as a fraction: the part we're interested in over the whole thing that could happen. In mathematical terms:

Probability=fracNumberofFavorableOutcomesTotalNumberofPossibleOutcomesProbability = \\frac{Number\\ of\\ Favorable\\ Outcomes}{Total\\ Number\\ of\\ Possible\\ Outcomes}

In our scenario, the total number of possible outcomes is the total number of months in a year, which is 12. The favorable outcomes are the months that start with the letters "J" or "M." Our mission, should we choose to accept it, is to count these favorable outcomes and then apply our probability formula. It’s like being a detective, but instead of solving a crime, we're solving a mathematical puzzle.

Now that we've laid the groundwork, let's roll up our sleeves and dive into the nitty-gritty of identifying those months and calculating the probability.

Identifying Favorable Outcomes

Alright, let's get down to business and figure out which months start with the letters J or M. This part is like a mini-brainstorming session where we list out the months and then filter them based on our criteria. Think of it as sorting through a deck of cards to find the ones that match a specific suit or number.

Listing the Months

First, let's list all the months of the year. This is our universe of possibilities, the complete set of outcomes we could randomly select from. Here they are:

  1. January
  2. February
  3. March
  4. April
  5. May
  6. June
  7. July
  8. August
  9. September
  10. October
  11. November
  12. December

We've got our full lineup now. Each of these months is a potential pick, but only some of them will help us solve our probability puzzle.

Months Starting with "J"

Now, let's zoom in on the months that start with the letter J. This is where we put on our detective hats and scan our list. We're looking for any month that kicks off with a "J." How many can you spot?

  • January
  • June
  • July

There you have it! We've identified three months – January, June, and July – that start with the letter "J." These are our "J" contenders, and they're definitely in the running to be part of our favorable outcomes.

Months Starting with "M"

Next up, we're on the hunt for months that start with the letter M. Let's put on our "M" goggles and scan the list once more. Can you spot the months that begin with an "M"?

  • March
  • May

Excellent! We've found two months – March and May – that start with the letter "M." These are our "M" champions, and they're also in the mix for our favorable outcomes.

Total Favorable Outcomes

Now comes the exciting part where we tally up our findings. We've identified the months starting with "J" and the months starting with "M." To get the total number of favorable outcomes, we simply add them together. How many months do we have in total that fit our criteria?

We have 3 months starting with "J" (January, June, July) and 2 months starting with "M" (March, May). So, 3 + 2 = 5. That means we have a grand total of 5 favorable outcomes. We're one step closer to cracking this probability puzzle!

With our favorable outcomes identified, we're now ready to plug these numbers into our probability formula and see what the final answer is. It’s like gathering all the pieces of a jigsaw puzzle and getting ready to fit them together.

Calculating the Probability

Okay, the moment we've been building up to – calculating the probability! We've done the groundwork of identifying our favorable outcomes, and now it's time to put it all together using our probability formula. Remember, probability is the ratio of favorable outcomes to total possible outcomes. It’s like figuring out your chances of winning a raffle based on how many tickets you bought.

Applying the Formula

Let's revisit our formula:

Probability=fracNumberofFavorableOutcomesTotalNumberofPossibleOutcomesProbability = \\frac{Number\\ of\\ Favorable\\ Outcomes}{Total\\ Number\\ of\\ Possible\\ Outcomes}

We've already figured out the key components. We know that the total number of possible outcomes is the number of months in a year, which is 12. We've also determined that the number of favorable outcomes – months starting with "J" or "M" – is 5.

Now, let's plug these values into our formula:

Probability=frac512Probability = \\frac{5}{12}

Voila! We've calculated the probability. The probability of randomly selecting a month that starts with the letter "J" or the letter "M" is 5 out of 12. It's like saying,