Can you can guess the month another person bought their Golf?

[Dubya]

Imagine someone unknown to you drove up in their Mark V Golf and said "I'll offer you odds of 10:1 that you cannot guess the month in which I took delivery of my Golf."

Even though your chances of picking the right month are only 1/12 (the year is not required), you guess May.

The person then says, let me tell you 10 of the months in which I did not take delivery of my car.

He then tells you every month of the year except August and May.

You now know the car was delivered in either August or May.

He then asks, "Would you like to stick with your original choice of May or switch to August?"

A group of onlookers has gathered.

People are yelling advice.

One, named Buller_Rock_v, is particularly vocal and says: "Stick with your initial choice! There are only two possible months now and only two choices; you have a 50/50 chance of winning now. You'll kick yourself if you switch and are wrong!"

Another person, Hawkie, says, "There was a 11/12 chance of you picking the wrong month in the first place. This has not changed now that you know 10 of the months that are wrong. There is an 11/12 chance that if you switch you will win, even though to some it looks like a choice between just two dates and a 50/50 chance!"

You hesitate.

There are only two options now. With only two months to choose from, it looks like 50/50.

But is it?

What would you do?