What are the chances that somebody would turn 10 on Oct. 10, 2010? Or 11 on 11/11/11? Or 12/12/12?
Rachel Wenninger will turn 10 years old on Sunday, Oct. 10, 2010.LUDLOW – Rachel Wenninger turns 10 on Oct. 10.
Rachel is in the fourth grade at Pioneer Valley Christian School in Springfield. She has three brothers and wants a hula hoop for her birthday.
There are many things that make her a special little girl.
And one of them is her birthday. Think about it.
She’s turning 10 on 10/10/10.
What are the chances of that?
Rachel says her favorite subject at school – besides recess – is math. But this question would stump even a budding mathematician.
What are the chances that somebody would turn 10 on 10/10/10? Or 11 on 11/11/11? Or 12/12/12? After that, it’s over, because there is no 13th month in the calendar.
Here’s how professor John Buonaccorsi, who teaches statistics in the Math Department at the University of Massachusetts in Amherst, sees it:
“If we ignore people born back in 1900, the match is only going to happen for those born in 2000, in later years ending in 01, 02, up through 12. The only ones that can have such a match in 2010 are those born on 10/10/2000.
“Of those born in 2000, 12 out of 366 – it was leap year – or about 3.3 percent, have had, or will have, such a match. Those born on 01/01/2000 turned 1 on 1/1/01, those born on 2/2/2000 turned 2 on 2/2/2002, et cetera.
“You can’t tell just how rare this is without additional information. If you ask what percent of the people in the total population have, or will have in the future, a match of this type – turning 10 on 10/10/10 or 9 on 09/09/09 – then you’d need to know how total numbers of individuals spread out across various years.”
At Western New England College in Springfield, math professor Richard S. Pelosi also says it’s hard to make an exact calculation without more info. Here’s how he approaches the puzzle:
“You have to multiply two probabilities together,” he says. “You’d have to know, of all the people living, what fraction were born in the year 2000.”
Of those children, only some were born on a “special day,” a day whose number matches the number of the month, such as April 4 or August 8. These special days only happen one day a month. So, to find how common they are, divide 12 by the number of days in the year, which comes out to about 1/30.
Then multiply that fraction by the fraction that tells what proportion of the entire population were born in 2000, and that will show how rare it is for somebody to turn 10 on 10/10/10.
“I guess the upshot is that it is not all that rare,” Buonaccorsi concludes.
Hmm.
OK, listen to this. In Rachel’s family, there are four children, and Rachel is the only girl. She has three brothers.
Her mother, Marie, was also the only girl in a family of four children. She has three brothers, too.
And her father, Steven, was the only boy in a family of four children. He has three sisters.
Now, what are the chances of that?