My Dreams are Riddles, Riddled with Math

A question on YA: "There are 120 customers in a store, 80 purchased at least 1 item. If 4 people are randomly selected, what's the probability all will buy at least 1 item?"

My Answer: The probability of any one customer having purchased an item is 80 out of 120 or 2/3. So if we are looking at parts of a whole, that represent all the possible combinations of events that could have occurred, then the part of this whole, where the first of the 4 people purchased an item, is 2/3 of the whole. Then the probability of finding a second person from the remaining crowd that also bought at least one item is 79 (because we already found one) out of 119 (again, because we have one less person to choose from in the crowd). The probability for the third person is found in a similar fashion...it would be 78/118 and 77/117 for the fourth person. We are each time finding an even smaller fraction of the whole that represents the final probability. If the probability for each was the same (independent events) then we could see that the area was decreasing exponentially (something I was never explicitly taught in school). To find the probability of all 4 people having bought at least 1 item, you need to find the product of the probabilities for each person. The answer then is 2/3 x 79/119 x 78/118 x 77/117 = approximately 19.25%.

Taking Count

Last time I heard, 2,752 people died in the 9-11 attacks (not including the 10 hijackers). According to Fixiraq.com, 3,592 US citizens have died in Iraq. I'm a mathematician so you'd have to tie my arms to keep me from crunching these numbers... That means that the losses in Iraq are now 130% of the number of people lost in 9-11. At globalsecurity.org you can get stats on the number of soldiers lost on a monthly basis. They made a graph of the data from May 2003 to February of this year and so I made a few amateur lines of best fit which gave me at least three reasonable equations, one of which was C = 1.74M + 38, where C is the number of casualties that month and M is the number of months since May 2003. That gives an estimate of 121.52 casualties in May and 123.26 in June. The true numbers? In May, 121 US deaths were reported in Iraq. In June 98 died. That suggests that, unfortunately, there does seem to be a positive correlation between our two variables...that is, the number of soldiers killed every month generally increases with time. However, this is only an estimate and, fortunately, in many months fewer soldiers died than the equation would lead us to believe. Little solace for the loved ones of those that did. Hmmm...Now, I wonder who is tracking the number of Iraqi civilian deaths?

Fuzzy Math Lesson

I looooove this! I've got to show my kids. A fabulous opening to a conversation on place value.