Question

What is the difference between Atleast and Atmost in Probability?

Answer 1

Hint: For solving this type of questions, firstly we need to understand the concept of probability and after that we need to understand the meaning of at least and at most and then observe some examples so that concept get more clear, after this all you can make the difference between at least and at most in probability.

Complete step by step answer:
Probability means possibility. The formula of probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes.
At least in the probability means, that all the probabilities that are larger than the given probability.
Whereas, At most in the probability means that all the probabilities that are smaller than the given probability.
So, we can say that at most means maximum, whereas at least means minimum.
We will understand it more with the help of some examples:
Let’s suppose three coins are tossed together and we have to find the probability of getting:-
1) At least one head
2) At most one head
So, the possible outcomes when three coins are tossed are as follows:
\[\{TTT,THT,TTH,THH,HHT,HTH,HTT,HHH\}\]
Now, for:
1) At least one head means the minimum number of heads is one (i.e. number of heads should be one or can be more than one)
So, the favorable outcomes of at least one head (means the minimum number of heads is one)
\[\Rightarrow \{THT,TTH,THH,HHT,HTH,HTT,HHH\}\]
2) At most one head means the maximum number of heads should be one (i.e. number of heads should not be more than one)
So, the favorable outcomes of at most one head (means the maximum number of head should be one or can be zero)
\[\Rightarrow \{TTT,THT,TTH,HTT\}\]
 Now, suppose we have given a dice and we have to find the probability of getting at most \[5\] and at least \[5\]
 So, the possible outcomes when a dice is rolled are as follows:
\[\{1,2,3,4,5,6\}\]
For getting at least \[5\] :
So, favorable outcomes of at least \[5\] (means that number on dice should be \[5\] or more than that)
 \[\Rightarrow \{5,6\}\]
For getting at most \[5\] :
So, favorable outcomes of at most \[5\] (means that number on dice should be \[5\] or less than that)
\[\Rightarrow \{1,2,3,4\}\]
Hence, by observing the above two examples, the difference between the at least and the atmost can be understood.

Note: Probability is used in our day to day life such as in game of cards, manufacturers use this theory to reduce the probability of failure, meteorologists use this to predict the weather conditions, in predicting natural disasters, in the world of sports it is used to predict which team will win.