Q#97: Large numbers in a raffle
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Suppose you enter a raffle held every weekday with just 200 tickets. You are only permitted to buy 1 ticket in each draw. Given this information, if you buy 200 tickets over 200 weekdays, what do you expect are your chances of winning at least one of the raffles?
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ANSWER
Can’t avoid stats and probability as a Data Scientist. This is one of those trick questions that seems easy at first glance but actually requires the advanced implementation of the Binomial distribution.
To answer this question, we need to consider some basic probability concepts. In our scenario, we have the following key information:
- The number of tickets available in each raffle is 200.
- You can purchase only one ticket in each draw.
- The raffle takes place every weekday for 200 days.
To calculate the probability of winning at least one raffle, we’ll approach this problem by considering the probability of losing each time and then subtracting that from 1. This approach is based on the complementary probability concept.
Calculating the Probability of Losing
To calculate the probability of losing in each raffle, we need to find the probability of not winning. In each draw, there are 200 tickets, and you have one ticket, so the probability of not winning is:
Probability of not winning = (Number of non-winning tickets) / (Total number of tickets)
Probability of not winning = 199 / 200
This means that in each individual draw, there is a 199/200 chance that you won’t win.
Calculating the Probability of Losing Over 200 Days
Since the raffle is held every weekday for 200 days, we need to calculate the probability of not winning 200 times consecutively. We can do this by raising the probability of not winning in a single draw to the power of 200:
Probability of not winning in 200 consecutive draws = (199/200)²⁰⁰
Now, let’s calculate this probability.
Probability of not winning in 200 consecutive draws ≈ (0.995)²⁰⁰ ≈ 0.0134
This means there is roughly a 1.34% chance of not winning in any of the 200 consecutive draws.
Now, to find the probability of winning at least once, we subtract this probability from 1:
Probability of winning at least once = 1–0.0134 ≈ 0.9866
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