Math+Travels+Answer+9

=Answer to Math Travels Question #9=

Here's my best guess as to the answer and how to find it:

First I found that there are 122 seats on the plane. 12 in first class (4 seats x 3 rows) and 110 in coach (5 seats x 21 rows).

Next, I found that 22 out of the 122 seats are middle seats. That means that you have an 18% chance of sitting next to 2 people and an 82% chance of sitting next to only one person.

Third, I found that sitting in a seat where you have only one person sitting next to you gives you a 1 in 121 chance to be sitting next to the puker (122 people on the plane, but you are one of them). That means that if you are in a middle seat, you have double that chance (2 in 121). Percentage wise, this comes out to 0.83% chance of sitting next to the puker for a non-middle seat, and 1.66% chance for a middle seat.

Now, the part that I'm a little unsure of...

The actual percent chance has to be somewhere between 0.83% and 1.66%. If there were equal chances of sitting in each seat, it would be right in the middle, but there is not an equal chance. There are 22 middle seats and 100 non-middle seats. By dividing 22 by 100 I found that you have a 22% better chance of sitting in the non-middle seat. So we should find an answer that is 22% of the way between 0.83% and 1.66%.

There are 83 hundreths of a percentage point between .83% and 1.66%. 22% of those 83 hundreths would be about 18 hundreths of a percentage point.

When you add those 18 hundreths to the 0.83% you get a...

__**1.01% chance of being randomly assigned to sit next to the one person who pukes on the plane.**__