While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Manchester United in the game. What is the probability that they were born within 25 miles of Manchester? Assume that: the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is ; the chance that a person born within 25 miles of Manchester actually supports United is ; the probability that a person not born within 25 miles of Manchester supports United with probability
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Manchester United in the game. What is the probability that they were born within 25 miles of Manchester?
Assume that:
- the probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is ;
- the chance that a person born within 25 miles of Manchester actually supports United is ;
- the probability that a person not born within 25 miles of Manchester supports United with probability .
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