Likelihood VS Probability

It may look simple, but it's capable to create head-scratching situations at times. Let's understand in a few words "What is what?".

For example, let's consider a normal distribution that has weight readings for class 12 students. The mean here is 65 kilograms and the standard deviation is 2.5. On the higher end, we have 73 kilograms and on the lower end, we have 57 kilograms. Now let's see what could be the possible questions for probability and likelihood.

Likelihood: L(Distribution | Data) or Likelihood of Data given the Distribution

L(mean=65 & sd=2.5 | student weight=68 kilograms). Here you could change the mean and standard deviation values and ask a question like, "What is the likelihood of a distribution with mean weight equal to 65 kilograms and standard deviation equal to 2.5 given that the weight of the student is 68 kilograms?". Here the values are determined using the corresponding y values for the x value.

Probability: P(Data | Distribution) or Probability of Distribution given the Data

P(student weight=68 kilograms | mean=65 and sd=2.5). Here you cannot change values for mean and standard deviation. The only value you are allowed to change is the student weight. So the question to be asked here would be, "What is the probability of a student weighing 68 kilograms if the mean weight of the class is 65 kilograms and the standard deviation is 2.5?". Here the value is determined using z-scores.