# Difference between Likelihood and Probability in this scenerio?

Lets say we have 100 people.

10 of them wear red.

20 wear blue.

70 wear green.

20 people from this group wear glasses.

We know that 3 people in the red group wear glasses and five people in the green group wear glasses. This means the other 12 who wear glasses are in the green group.

If I was blindfolded and selected one person from the red group, what is the probability I will select a person with glasses?

If I was blindfolded and selected one person from the red group, what is the likelihood the person I selected will be wearing glasses?

If all three groups were combined and I selected one person while blindfolded, what is the probability and likelihood of selecting a red person with glasses?

Also, how can I calculate this in excel?

• Can you rephrase your questions? Because probability that the red group will have someone who wears glasses will be surely $1$ since we know that there are people who wear glasses in the red group. – gunes Jan 30 at 18:46
• OK, I see that now. I reworded it. I think this is more of what I'm looking for. – Melissa Blaze Jan 30 at 21:54

To put it simply, I don't see a difference between the following two questions:

• What is the probability of getting heads if you toss a fair coin?
• What is the likelihood of getting heads if you toss a fair coin?

So, the answer to your first and second questions will be the same: $$P(\text{Selected One is with Glasses|Selected one is from Red Group})=P(G|R)=\frac{P(R\cap G)}{P(R)}=\frac{3}{10}$$

The third and fourth questions, we simply seek for $$P(R\cap G)=\frac{3}{100}$$

In Excel, it's just a matter of assigning cells to each of these probabilities, and applying the formulas.

There are some other uses of the keyword likelihood together with other keywords like posterior, prior, evidence etc. although your question doesn't seem to go that much deep.