# Math Geek Mom: Expectations

There is a concept in statistics called “expected value.” This is the expected outcome of any situation that involves probability, and is found by multiplying the possible outcomes by the probability that each will occur and then adding these products together. Expected value calculations are why it is generally thought that one should not play the lottery, as some claim that the lottery is a “tax on people who did not do well in math

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July 26, 2012

There is a concept in statistics called “expected value.” This is the expected outcome of any situation that involves probability, and is found by multiplying the possible outcomes by the probability that each will occur and then adding these products together. Expected value calculations are why it is generally thought that one should not play the lottery, as some claim that the lottery is a “tax on people who did not do well in math.” Even the seemingly greatest payoff, when multiplied by the probability of winning (which goes down as more people buy tickets to get into high-paying lotteries) has an expected value that is probably less than the cost of purchasing a ticket. I found myself thinking of this recently after I had two of my daughter’s friends over to play with her one evening. As the evening unfolded, it became very clear to me that I was quite outnumbered. And it was not hard for me to remember that we had once had an “expected value” of having three children. Thank heavens, I thought, that I generally had to manage only one (relatively well behaved) child!

I realized long ago that life does not always work out as planned. Before we married, my husband and I hoped to have a handful of children, but in the end were ecstatic to adopt one daughter. I had hoped to earn tenure at my first job, but found my efforts derailed by a run-in with a brain tumor that announced its presence on the morning of the first day of classes of that first job. And my plan of earning tenure before getting married and having children did not work out as expected, either, although I did earn tenure at my second job only a few months before we brought our daughter home. I found myself thinking of expectations in life last week, when the most horrible, unexpected event occurred in a movie theater in Colorado.

When I heard of the shootings in the Batman movie last week, I was struck with horror as well as a little guilt. I had written a blog column last Thursday complaining about the nastiness of the current election, and posted it without any thought of what was to happen before the blog was published. When I heard of what had happened overnight, the whole line of thought seemed extremely trivial and petty, as I realized that it was hardly worth saying. Indeed, the candidates seemed to agree, as they stopped the procession of political ads for a few days, especially in Colorado, which I soon learned was a fellow “swing state.”

And so, I want to take a second to acknowledge the horror that unfolded one week ago, and to send my condolences to the families of those who were murdered or injured. I am left with the same sense of helplessness and horror that I felt earlier this year when a teenager shot and killed four classmates in a high school not far from where I live. Again, I am struck with the thought that surely we can do a better job in creating a peaceful world. Does anyone have any thoughts on how to do that, and what measures we can all take to make it happen? I hope for a world where I can take my child, and perhaps, if I am brave enough, a few of her friends, out for the evening without worrying about our safety.

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