Birthday Paradox Question

GRE Quant Problem Solving
1

If the probability of being born in a particular month is equal to all other months of the year, what is the minimum number of people needed in a room so that the probability that at least two people share a birthday month is greater than 0.50?

I did not understand Greg’s solution to the above question in the PrepSwift: The Birthday Paradox quiz. Where is 13-n coming from? Why can’t I just do 12/12*11/12… and keep multiplying the decimal values of each fraction until I hit a value less than 0.50 and take the value just before that. By this method, I got 9.

Also, should we expect questions like this on the GRE?

image
image1402×1104 45.5 KB

2

Try putting n = 1, 2 and 3 and see what you get.

We are doing that actually. Check your work.

Of this type? I’d say no, though you might get pieces of this question instead.