I want to know what the probability is given a family having 4 children, that one child has a birthday this month (at any given time)
How would this be expressed as an equation?
How do you account for the likelihood that 2 or more children have a birthday in the same month?
Lastly, can this be answered mathematically (and accurately) without knowing statistics about what percentage of the world is born in January, February, March, etc.?
This is not a homework assignment, this question arose when talking to my son about a family friend who has 4 children, it seems that one of them is always having a birthday.
We want the probability that at-least one child has a birthday in June.
This is equivalent to the total probability, minus the probability that no child has a birthday in the month of June.
$$1-(\frac{11}{12})^4 = \frac{6095}{20736} = \text{approx} \;\;29.39\% $$
Note: This assumes that all of the children are born in each month equally likely. Hence without statistical research. User $André$ raises a very valid concern in regards to the possibility of doing such a problem without the above assumption.