I found out my girlfriend was lying about one guy.
For months, she kept saying he was just a friend, and honestly I believed it enough to not make it a daily issue. Not fully, but enough.
You know that weird place where something feels off, but you also don't want to become that insecure person who questions every name?
Then one night, her phone was on the table and his notification came.
“Reached home?”
That message alone was not proof of anything. People can ask that. Friends can ask that. I was still trying to be normal about it.
But then I remembered she told me she was out with her cousins.
So I asked casually, “Who dropped you?”
She said, “My cousin.”
I asked which cousin.
She paused.
That pause did more damage than the message.
After that, the story started changing as she spoke. First it was cousins. Then it was cousins and friends. Then he was there too, but only for a while.
Then it became, “Actually, he dropped me because it was late.” Then somehow I became insecure for even asking.
Bro, I was literally watching the probability update in real time. The notification changed it a little. Then the pause changed it even more.
By the time the story changed for the third time, the calculation was basically done.
That is Bayes theorem.
Bayes theorem is what happens when you start with a belief, observe new evidence, and update that belief.
Formula:
P(H | E) = (P(E | H) × P(H)) / P(E)
Where:
- H: Hypothesis
- E: Event (what you observe)
- P(H): Prior probability
- P(E): Overall probability of event
- P(E|H): Prob. of event if hypothesis was true
- P(H|E): Probability hypothesis is true given event (updated belief)
Let's take an example and solve it step by step:
Suppose your girlfriend is honest 95% of the time and lies 5% of the time. She avoids eye contact 30% of the time when she is honest and 80% of the time when she is lying.
If she avoids eye contact, find the probability that she is lying.
Step 1: Define Hypotheses
- H1: She is honest
- H2: She is lying
Step 2: Define Event
- Event (E) = She avoids eye contact
Step 3: Write Priors
- P(H1) = 0.95 (honest)
- P(H2) = 0.05 (lying)
Step 4: Write the Likelihoods
Avoids eye contact when honest
- P(E | H1) = 0.30
Avoids eye contact when lying
- P(E | H2) = 0.80
Step 5: Calculate the Total Probability
P(E) = P(E|H1)×P(H1) + P(E|H2)×P(H2)
P(E) = (0.30)(0.95) + (0.80)(0.05)
P(E) = 0.285 + 0.04
P(E) = 0.325
Step 6: Apply Bayes Theorem
- P(H2 | E) = (P(E | H2) × P(H2)) / P(E)
- P(H2 | E) = ((0.80)(0.05)) / 0.325
- P(H2 | E) = 0.123
Final Answer:
If she avoids eye contact, the probability that she is lying is 12.3%.
Congratulations, you have just learned Bayes theorem!
The way Ronaldo will be eager to score against DR Congo tomorrow after that Messi banger, all the fans that will be behind the Goalposts should go to the stadium with Helmets