Pistacchio loves to celebrate its birthday.
Depending on your mood, you can either embark on celebrations oozing with luxury and exaltation, or settle for more ascetic, modest, and mundane events.
Yesterday, for example, undecided between waste and sobriety, he flipped a coin.
To give you a brief summary, the party consisted of the following:
07:00 AM rocket race with Bezos, Musk and Branson, departing from Cape Canaveral “round trip to Santa Teresita”. Win and take the opportunity to write with your vapor trail “Tax the (other) rich” above the IRS building.
10:00 AM blocks China Suarez on Instagram
10:15 AM Have breakfast with Trump and Biden at the White House. Trump says “Believe me, this has been the best breakfast in the history of breakfasts, maybe ever.” Biden says “can I have an autograph”? and offers you the back of the declaration of independence.
10:25 AM Nicholas Cage is detained by the secret service while stealing the declaration of independence.
11:00 AM Play the Squid game and put all the beds under the ball with the won. He leaves in 5 minutes with the silver and Kang Sae-byeok.
12:15 PM Salt Bae prepares lunch for you.
02:00 PM Block China Suarez on TikTok
02:15 PM Ski for a while in Aspen. It breaks the speed record, but it does it uphill “if you think about it, downhill gravity does most of the work.”
04:20 PM Host Saturday Night Live. They record it on a Monday afternoon for being him. Margot Robbie refuses to kiss him in a sketch, saying “I don’t like odd numbers, let’s try 16”.
05:00 PM He plays a tribute basketball game and Scottie Pippen asks him to autograph the pants with which Michael Jordan retired.
05:15 PM Someone brings Jordan a robe so he can go home.
05:20 PM Block China Suarez on Imgur
05:20 PM Nap on a Concorde heading to Europe
08:30 PM: jump from the plane and hurt like a fireball into the sky of Paris.
8:31 PM: Slow down a bit for Gal Gadot to tie his tuxedo bow in mid-flight. They break two records for aerial acrobatics and one for longest kissing.
08:32 PM: true to his motto “the parachute is for beginners” he positions his body in order to generate aerodynamic resistance and lands in the princes’ park, at the exact point to head a Messi cross that had come past. Pistacchio’s goal in the 47th of the second half.
09:00 PM: Arrives at Alain Ducasse at the Plaza Athénée, where the Rolling Stones, Taylor Swift and two of the Mambrú boys await him playing.
09:30 PM: Dinner with family and friends.
10:00 PM He signs books with Taleb, Kanheman, Harari and Ariely, while discussing the contribution of the Levantine intellect in 21st century behavioral psychology.
10:30 PM: It is agreed that you have to write a “Pistacchio problem” for the N5 Now selection process. He does it in the elevator as he goes up to his room.
11:00 PM Unlock the door to the room. Enter China Suarez.
Enough with the story of the modest birthday. One day I will tell you the luxurious one. But now we come to the problem.
Pistacchio wonders two things:
Questions:
- What is the minimum number of people that must be in a room so that the probability of two having their birthday on the same day is greater than 50%?
- What is the minimum number of people that must be in a room so that the probability that one will have a birthday on November 22 (Pistacchio’s birthday) is greater than 50%?
Answers:
23 y 253
Most people overestimate the first number and underestimate the second.
Let’s go to the first one: It takes only 23 people to have a 50.7% probability that there will be a repeat birthday.
Let’s imagine that we are adding people one by one to the room. The second person we add will have only 1/365 probability of meeting the same day as the first. But as we add more people, each one has an increasing possibility of fulfilling the same day as ANY of the previous ones.
For example, person 20 has 19 people to match, person 23 has 22 (where 50% cumulative probability is reached), and so on. Upon reaching the 75th person, it is virtually impossible for everyone to have been born on different days (a probability in 10 million).
It is precisely this effect that explains why the second number is so high. Although we intuitively think that if we put 183 people in the room we make sure that we have more than 50% of the days occupied, the truth is that many of them will turn years on repeated days.
Although this problem requires a complex calculation involving factorials to arrive at accurate results, the options were designed for
