Question

What is the difference between at least one head and at most one head in probability?

Answer 1

Hint: Probability is defined as the event likely to occur. It is the ratio of favorable outcomes to the total possible outcomes. Here, at least one means it can be greater than one and at most one means it can be zero or one but not more than one. Here we will take one example to understand it clearly.

Complete step-by-step answer:
Let us take an example, where three coins are tossed together then find the probability of getting –
I.At least one head
II.At most one head
Here first of all find the possible outcomes when three coins are tossed, there are a total eight outcomes.
Possible outcomes – TTT, THT, TTH, THH, HHT, HTH, HHH, HHT
Now, at least one head means the minimum number of heads should be one or more.
The favorable outcomes are THT, TTH, THH, HHT, HTH, HHT, HHH ….. (A)
Now, at most one head means the maximum number of heads should be one or less than one.
The favorable outcomes are TTT, THT, TTH, HTT ……. (B)
Hence, (A) and (B) are the required solutions to understand the difference between at least and at most one heads.

Note: Don’t get confused between the terms at least and at most. Least means the minimum small number the border or the limit to start with and at most means the number or limit maximum it can hold. Understand the words properly. Always take the reference example to understand the concepts.