What is the probability of a random test occuring on any of the first 5 days of a 31 day month?

Question

Hypothetically, if you know that you will be given a test on any random day in March, but you also know you will no longer be in that class after March 5th, what is the probability that you WILL have to take the test?

Answer 1

The probability that the test occurs on any particular day in March is 1 out of 31, or 1/31.

The probability that the test occurs on any one of five days, regardless of when in the month that day occurs, can be viewed as an OR probability. That is, the test day could be March 2 OR March 8 OR March 17 OR March 23 OR March 39, etc.

Notice also that if the test occurs on a particular day, it can't/doesn't occur on any other day.

In statistical terms, the event of the test occurring on one day and the event that it occurs on another day are mutually exclusive (disjoint).

With OR probabilities that are disjoint, we sum the individual probabilities. So:

Prob (test occurs on Mar 1 OR Mar 2 OR Mar 3 OR Mar 4 OR Mar 5) = Prob (test on Mar 1) + Prob (test on Mar 2) + Prob (test on Mar 3) + Prob (test on Mar 4) + Pro (test on Mar 5).

= 1/31 + 1/31 + 1/31 + 1/31 + 1/31

= (1/31) * 5

= 5/31