What is the probability that in a group of six people at least two were born in the same month?

For ease of answering, we will work under the assumption that the probability of someone being born within any given month is equal to that of any other month.

Allowing that assumption, we can look at that question a slightly different way and say "What is the probability that all people in a group of six would each be born in a different month?" The answer to that would be 12/12 * 11/12 * 10/12 * 9/12 * 8/12 * 7/12, which can also be expressed as (12! / 6!) / 126, and comes out to 665280 / 2985984, which equals 385 / 1728.

The probability of at least two being being born in the same month would then be:

1 - 385 / 1728

= 1343 / 1728

≈ 0.7772, or approximately 77.72%