What is the Difference between Atleast and Atmost in Probability?

The answer to ‘what is the difference between atleast and atmost in Probability?’ is “at least” means the event occurs a minimum number of times or more, while “at most” means the event occurs up to a maximum number of times or less. For example, “at least 3” means 3 or more, and “at most 3” means 3 or fewer.

Complete Answer:

Probability is a way to measure how likely something is to happen. It’s like saying, “What are the chances of this thing happening?” We use numbers to show probability, from 0 (it will never happen) to 1 (it will definitely happen).  

Now, let’s talk about the difference between atleast” and atmost in probability. These phrases help us describe a range of possible outcomes.

At least in Probability: This means “the minimum amount or more.” Imagine you’re rolling a die. If you want to know the probability of rolling “at least a 4,” that means you’re looking for the chances of rolling a 4, 5, or 6.

At most in Probability: This means “the maximum amount or less.” If you want to know the probability of rolling “at most a 3,” that means you’re looking for the chances of rolling a 1, 2, or 3.

Examples to Explain Atleat and Atmost in Probability

Example 1: 

You have a bag with 5 marbles: 2 red, 2 blue, and 1 green. What’s the probability of picking at least one blue marble if you pick two marbles?

Answer: Here is how to solve this probability problem:

1. Total Possible Outcomes:

First, we need to figure out how many different ways there are to pick two marbles from the bag. This is a combination problem (order doesn’t matter). We have 5 marbles and want to choose 2. The formula for combinations is:

nCr = n! / (r! * (n-r)!)

Where n is the total number of items (5 marbles) and r is the number we want to choose (2 marbles).

5C2 = 5! / (2! * 3!) = (54321) / ((21) * (32*1)) = 10

So, there are 10 possible ways to pick two marbles.

2. Outcomes with Atleast One Blue Marble:

“Atleast one blue” means one blue marble or two blue marbles. Let’s look at the possibilities:

• Two Blue: There are 2 blue marbles, and we want to pick 2. 2C2 = 2! / (2! * 0!) = 1 way (Blue, Blue)
  
• One Blue: We pick one blue marble (2 choices) and one marble that isn’t blue (3 choices: 2 red + 1 green). 2 * 3 = 6 ways (Blue, Red), (Blue, Red), (Blue, Green) – note there are two red marbles
  

3. Calculate the Probability:

• Favorable outcomes (at least one blue): 1 + 6 = 7
• Total possible outcomes: 10
• Probability = (Favorable Outcomes) / (Total Possible Outcomes) = 7/10

Therefore, the probability of picking atleast one blue marble is 7/10.

Example 2: 

You are flipping a coin twice. What’s the probability of getting atmost one head?

Answer: Here is how to figure out the probability of getting atmost one head when flipping a coin twice:

1. List all possible outcomes: When you flip a coin twice, there are four possible outcomes:
   
   • HH (Heads, Heads)
   • HT (Heads, Tails)
   • TH (Tails, Heads)
   • TT (Tails, Tails)
     
2. Identify the favorable outcomes: “Atmost one head” means zero heads or one head. The outcomes that fit this description are:
   
   • HT (Heads, Tails)
   • TH (Tails, Heads)
   • TT (Tails, Tails)
     
3. Calculate the probability:
   
   • Number of favorable outcomes: 3
   • Total number of possible outcomes: 4
   • Probability = (Favorable Outcomes) / (Total Possible Outcomes) = 3/4

So, the probability of getting atmost one head when flipping a coin twice is 3/4 or 75%.

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