I have no clue how to solve a probability question.

This isn't related to a test or anything, just a personal one. A local radio station does "Birthday Bucks" 3 times a day, 5 days a week for 3 months. What is the likelihood that my own birthday and my daughter's birthday are called on the same day as an annual event? I'm not sure if this matters but our birthdays were called out sequentially. One in the morning time slot and the other in the afternoon time slot and no one we knew in the evening time slot.

The reason for my question is because my daughter passed away unexpectedly and the annual event was of importance to me.

Re: I have no clue how to solve a probability question.

[To start with, someone else should check these results. Thanks!]

I made some assumptions:

- You and your daughter had different birthdays

- All 366 birthdays (including Feb. 29) have an equal probability of being called

- The station does not repeat birthdays within each day (however, they may from day to day)

With these assumptions I got the following:

(a) The probability of your and your daughter's birthday being called on the same day: $\displaystyle \frac{1093}{24313380} \approx 0.0045\%$

(b) The probability of your and your daughter's birthday being called sequentially (on the same day): $\displaystyle \frac{243}{8104460} \approx 0.0030\%$

(c) The probability of your birthday being called in the morning and your daughter's birthday being called in the afternoon: $\displaystyle \frac{1}{133590} \approx 0.0007\%$

**This amounts to the following:**

(a) will happen (on average) once every 556 years (about 7 life times*)

(b) will happen (on average) once every 834 years (about 10 and a half life times)

(c) will happen (on average) once every 3340 years (about 42 life times)

[* assuming 80-year life times]

I'm very sorry for your loss, and I hope this helps. By the way, all of these are *well* below the standard statistical significance of 5%. This was a truly anomalous event.