Mathematical Exploration topic: The Birthday Paradox Objective: To understand the chance of two people having the same birthday in a set of a determined amount of random people. 2) Justification: The main objective of the birthday paradox is to use different applications to show the chances of 2 people having the same birthday, even though most people think it’s a 50%, it’s actually not because we need to involve all of the possible chances of birthdays meaning everyday of the year, not including leap year( February 3). The most interesting part of the birthday paradox might as well be that it is calculated using the probability that every birthday is different, because both probabilities are parallel. Another interesting part about this paradox is that instead of the probability of two people having the same birthday decrease as more people are added as we can see from an every day life problem such as taking a slice of pizza from a whole, the chances increase as there are more people available for having the same birthday, which automatically makes the results a linear graph. 3) Introduction: In this math exploration, I will use mathematical probability applications to solve the birthday paradox. From …show more content…
One of them the probability of success over the total amount of outcomes. Since the probability of each outcome or day depends on whether the day before was already used, it is necessary to apply the formula for the probability of two dependent events. According to the textbook, Advanced Mathematical Concepts, precalculus with mathematical application, “ if two events, A and B, are dependent, then the probability of both events occurring is the product of each individual probability.” Because, the probability that every birthed is different and the probability that at east two people or more will have the same birthday is complementary, we use the formula 1-P( every birthday being