I am not sure whether I have approached this question correctly... I would appreciate your input on my answer and any suggestions regarding any other calculations I should be doing. Thanks in advance.

Question:

Evidence has been produced that famous people are less likely to die in the month of their birthday than in other months. The (skeptical) hypothesis is that dying is equally likely in any month regardless of birthday. Suppose that out of 120 celebrities 7 died in the month of their birthday. Imagine a hat with 12 cards, each card a month, as well as a list of the 120 celebrity birthdays. We shuffle and pick a card, noting whether it matched the first celebrity birth month. We then repeat this (replacing the card each time, of course), each time noting whether the month picked from the hat matched the next birth month, etc., until we have gone all the way through the 120 names on the list.

Then we repeat this procedure 100 times, each time recording how many matches we got between the 120 picks from the hat, and the list of 120 birthdays. We got the following frequency distribution. What is your conclusion and why?

The column on the left represents the number of celebrities dying in their birthday month (6, 7, 8 etc). The column on the right represents the frequency. (1, 3, 9 etc). (I cannot paste the table properly here - if there is a way of doing this, let me know).

6 1

7 3

8 9

9 20

10 32

11 25

12 7

13 1

14 2

My answer so far:

The probability of observing 7 or fewer matches (celebrities dying in their birth month) is 4/100 = 1/25.

I do not know if this is correct or enough to answer this question sufficiently.