It’s Your Lucky Day: We’re Talking Probability

Mar 2, 2022 | South Friendswood

Is luck real? We are appreciators of math at Mathnasium of Friendswood, which means that we like to think of luck in terms of probability. And probability is not luck. You may know someone you’d consider lucky. Maybe they get the perfect parking spot more often than you’d expect. Maybe they seem to remember their umbrella when it happens to rain. Maybe they win the lottery. Here at Mathnasium, we think this “luck” may be simply a product of probability. Today we discuss why.  

Luck is much like chance. What are the chances that you will experience your desired outcome? Believers in luck may think that math is not involved in this “calculation,” but the chances of experiencing a particular desired outcome are very concrete. We calculate probability by dividing the number of desired outcomes by the number of total possible outcomes:   




So, if I were to open a bag of M&Ms, and hoped to get a lucky green one when I reached inside, I could calculate the exact probability that I’ll get what I want. A typical Sharing Size M&M bag may contain 109 candies, divided by each color as follows:  

  • 14 brown   

  • 21 blue  

  • 19 yellow  

  • 23 green  

  • 15 red  

  • 17 orange  

My odds are good if I want green! It seems to be the most popular color in this particular bag. Could I get six green candies in a row? Sure! Odds are not great, but they’re not zero either. If I want a green candy on the first try, the probability I have is 23/109. After I eat the first green candy, I have to remove one of the greens from my “desired” category (I ate it, so it’s gone!), and I also have one fewer candy in the total. Now my odds of getting a green candy again are 22/108. Is it possible for me to get 22 more greens in a row? Technically, yes! But it’s not probable. With each green candy I remove, my probability decreases, until I have only one green candy left to get in a bag with 87. Retrieving the final green M&M in the bag is far less probable now than getting the first green M&M was.  

The isolated odds of drawing a green M&M each time I reach for one are straightforward. Desired outcomes/possible outcomes. However, we also have to consider the probability of getting green M&Ms consecutively. When we calculate the probability of getting a green candy the first time, it’s 23/109 (nearly one in four); the second green candy is 22/108 (closer to one in 5). To figure out how likely we are to get them one after another, we have to multiply the two fractions. The odds that we draw one green after another for the first two M&Ms are 506/11,772, or 253/5,886 (close to one in 24). As we progress through calculations, the chances get exponentially smaller that 23 green candies come out first. Luck is when the low probability of something happening is unexplainably defied. Snagging 23 green M&Ms in a row from a bag containing 109 candies is undeniably lucky because of just how improbable it is. 

When it comes to the lottery, probability rules. While one “lucky winner” defies their odds as an individual, it only makes sense that somebody buys the winning ticket if enough people play. The Powerball Mega Millions record jackpot was $1.586 BILLION in January 2016, when multiple winning tickets ended up splitting the prize. In January 2018, it was a measly $450 Million, and the probability of winning was 1 in 302.5 million. Even with such slim odds, if there are 302.5 million lottery tickets sold, someone is statistically likely to win. And that’s probability, not luck. Chances for “getting lucky” and winning the lottery are slim, but they are not zero.  

At Mathnasium of Friendswood, we have carefully designed our methods and programs to create our own luck for success. Increase the odds of your child’s achievement by enrolling in one of our programs today! Call us at (832) 569-5073 to schedule a risk free assessment!