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Ricardo (4s): Hello, everyone. Welcome to the five minutes PM Podcast and continuing Today the series about Cognitive Bias So. As I promised last week, I will do a small exercise to you to show how our brain sometimes does not make the best mathematical decision. And this example is a very popular example called The Birthday Paradox. So let's do an exercise. So look, first, if you don't like math, please take a piece of paper just to write down some formulas. They are very basic. Okay. But if you want just write down, otherwise just try to follow with me. Ah, it's not easy to do that in a podcast, but try to follow with me, and you will get what I mean with that.
Ricardo (50s): Imagine that you enter it in a room and you see inside this room, 22 people, you are the 23rd. So among these 23 people, what is the probability that at least two people share the same, I will repeat the same anniversary the same month and day of Birthday. So think about it. Most of us think that the probability of finding in a group of 23 people, two people with the same day and month of Birthday it's quite rare, it is quite unusual. So some of you may say that 2%, 3%, 5%, 10%.
Ricardo (1m 34s): So let's go to the math and let's try to understand what is the real probability of that. So the first thing we need to start is, what is the chance that a person "A" has the same day and month of Birthday of person "B"? What do you agree with me that the chances of matching the dates is one in 365. Imagine that the year has 365 days. So just one that day in that month. So if I ask you, what is the chance of not matching? So it's basically 364 out of 365, right?
Ricardo (2m 19s): So during a 364 days out of the whole year, you will not match. So this is basically 99.726%. So this is the chance that to people do not match an anniversary white rational, right? If I will ask you to do that, you won't say maybe 1%, maybe this. So it's not very different, right? It's not very different. So the chances that to people do not meet it's quite high. So when you see someone that has the same date you celebrate, right? But now let's take the second conflict.
Ricardo (2m 59s): How many pairs of comparison do we have if we have two people there is only one pair You in the other person, but let's suppose you have John Ana an Emmy. So you have three pairs to compare Jon with Anna, Jon with Emmy, and Emmy with Ana So three. So we maybe four, five, six, seven. So imagine 20, you need to compare a personal one with person two, person one with person three, person one with person four, person one with person five. And there is a formula for that. The Formula is the size of the group times the size of the group minus one, divided by two.
Ricardo (3m 44s): So if you have 23 people, it's 23 times 22 divided by two. So you need to evaluate 253 pairs. So you read to evaluate these 253 pairs to see if any of them match in the formula is you take the chances that they don't match 364 out of 365. And you take that exponential and the factor of 253. So this is the chance that one of them will match and surprising this is point 4995.
Ricardo (4m 31s): It means with a group of 23 people there is more than 50%. That is one minus 0.4995 of chances that at least two people will have the same Birthday so look, how crazy is this? Because many times when you are in this a small group in a party and you want to play this game, just do that. And you will be surprised at that. Maybe someone who say, Oh, your birthday, and it is the same all of my father or, or my son. So this is exactly the Paradox. And look, if you have a group of 50 or more people, these increases to 96%.
Ricardo (5m 11s): So it's almost impossible. It's 4%, 4% chance that people do not match 80 people. 99.98 So means If you have 80 people, it's almost impossible that you do not find at least a pair with the same date. And why I showed this? this is just to show you how our Cognitive Bias influences us so many times when we are doing risk analysis or we are doing an assessment. We do not go back to the math and try to understand data, but we use our feelings of this. I don't want to explain this because I'm an engineer, but some people think that this is ego or this is a flip thinking that we are so special that nobody else can have the same Birthday date as us.
Ricardo (6m 4s): That this makes us blindfold to reality that in a group of 23 people there is more than 50% chance that we'll meet someone. Go to Google and put Birthday Paradox and you will see all the formulas. And if you want to study a little bit of statistic, but this is just to show you how deep sometimes our Cognitive Bias is on us, that drives us to make wrong and non-informed decisions. And this will drive your project and your product development to failure. Next week, I will talk about the Dunning Kruger effect and the imposter syndrome.
Ricardo (6m 44s): Two opposite terms that also will drive you crazy. If you do not understand very well, how to handle them and make better decisions. So see you next week with another five minutes PM. Podcast.