People interested in seeing the Broadway musical Hamilton — and there are still many of them, with demand driving starting ticket prices to $\$600$ — can enter Broadway Direct’s daily lottery. Winners can receive up to 2 tickets (out of 21 available tickets) for a total of $\$10$.
What’s the probability of winning?
How easy is it to win these coveted tickets? Members of NYC’s Data Incubator Team have collectively tried and failed 120 times. Given our data, we cannot simply divide the number of successes by the number of trials to calculate our chances of winning — we would get zero (and the odds, which are apparently small, are clearly non-zero).
This kind of situation often comes up under many guises in business and big data, and because we are a data science corporate training company, we decided to use statistics to determine the answer. Say you are measuring the click-through-rate of a piece of organic or paid content, and out of 100 impressions, you have not observed any clicks. The measured CTR is zero but the true CTR is likely not zero. Alternatively, suppose you are measuring the rate of adverse side effects of a new drug. You have tested 40 patients and haven’t found any, but you know the chance is unlikely to be zero. So what are the odds of observing a click or a side effect? Continue reading