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Hello everyone.
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In this lesson, we'll tackle an intriguing probability problem, estimating the chance that among the 80 ,000 marriages that took place in new york last year, at least one couple both had their birthdays on april fool's day.
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Probability challenges like these not only test our mathematical intuition, but also our ability to apply logical assumptions and calculations to real -world scenarios.
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So let's dive into this problem with a step -by -step approach.
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Setting up assumptions.
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Assumption 1.
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For simplicity, assume that birthdays are evenly distributed across the 365 days of the year.
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This means each day, including april 1st, has an equal probability of being someone's birthday.
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Assumption 2.
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Assume that the birthdays of the two partners in a couple are independent events, meaning the birthday of one partner does not influence the the birth date of the other.
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Calculating the probability for one couple.
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The probability of one partner born on april 1st.
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Given our first assumption, the probability of one person being born on april 1st is 1 out of 365 days.
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Possibility of both partners born on april 1st...