Over a period of years, a person has 74 appointments. They inadvertently miss 5 of these.
The 5 missed appointments all occur in warmer weather. Of the total 74, 44 of these appointments are in warmer weather, and 30 are in cooler weather. This distribution is because of the seasons – there are more warmer months than cooler. However there is little difference between the overall monthly average of appointments between the warmer and cooler months, 6.29 average per month vs. 6 respectively.
The end question is: what is the probability / likelihood that the missed appointments occurring on warmer days was or wasn’t by chance?
Is this the same probability question as the following:
a person is asked to select 5 cards at random out of a pack of 74 cards, 44 of which are red, and 30 black … and what is the probability they select 5 red cards?
Using a sequentially reduced probability as red cards are removed, the combined probability of all cards being red:
0.595 * 0.589 * 0.583 * 0.577 * 0.571 = 0.0674
And is this the correct way to look at it? Or should the total no. of appointments, warmer & cooler days reduce as time goes on?
Which is the better way to answer the end question as above?