Probability vs likelihood

Link: Probability

Probability §

Probability reflects the area in the distribution. E.g.

$$p(\text{weight > 32}\mid \mu =32,\sigma =2.5)$$

The left side focus on the x variables on the distribution, while the right side of bar represents the shape of distribution. So, a change in left side will get us a new probability.

Likelihood §

Likelihood is the dot (y value) in the distribution. The notation is:

$$L(\mu =32,\sigma =2.5\mid \text{weight > 32})$$

If we modify or shift the distribution, we will get a new likelihood.

Conclusion §

In short, the probability fixs the shape of distribution while checking how much chance of x happening. On the other hand, the likelihood fixs the x variable and the distribution can be moved.