# How does likelihood differ from probability? [duplicate]

i.e. Tossing a fair coin

$$p_H =$$ probability of heads $$= 0.5$$

$$L(p_H | HH) = P(X = HH | p_H)$$

$$= 0.25$$

Okay, right-hand of equation I understand,

$$P(X = HH | p_H) = 0.25 =$$ probability of "$$X = HH$$" given $$p_H$$

but what does the value resulting from the left side mean if it's not probability.

$$L(p_H | HH) = 0.25 =$$ Likelihood of $$p_H$$ given we observed $$HH$$ is $$0.25$$ ??

What does that even mean? Certainly it's not the same as $$P(p_H | HH)$$

• stats.stackexchange.com/questions/2641/… Jan 15, 2020 at 18:21
• weird that didn't show up when i was typing the question Jan 15, 2020 at 18:27
• Agreed: it looks like the pop-up search is pretty bad.
– whuber
Jan 15, 2020 at 18:46