What are your Chances? by Laurie Townsend

When you play a game do you know if the game involves chance and what your chance of winning will be? Let’s look at some common types of chance involved in games. There is the coin toss. There are 2 choices, head or tails. The chance is 1 in 2 or a 0.5 probability of either outcome. No matter how many times you toss the coin every time it will be 0.5 chance. 1

What about dice? What chance is involved in throwing a die? For one die it is 1 in 6 because there are 6 possible outcomes. For 2 dice there are 36 outcomes. So the chance of getting two 1s is 1 in 36. To find that mathematically you multiply the number of outcomes together. 2 die have 6 outcomes, so it is 6 x 6 to find the number of outcomes, 36. With 3 dice it would be 6 x 6 x 6 to find the total number of outcomes. Again, there is no skill involved only chance. 2

1 2 3 4 5 6 7 What if you have a game with a spinner? If the spaces on the spinner are all even and the choices are unique then your chances are 1 in how many choices are on the spinner. If the game spinner has 7 spaces that offer 7 unique outcomes and the spaces are equal in size then your chance is 1 in 7. If the spaces were of unequal size the chance would be different and if the some outcomes were identical the chance would be different. 1 2 3 4 5 6 7 3

Games with cards offer many possibilities of outcomes depending on what you are looking for. A standard deck of playing card has 52 unique cards. If you want one card out of the deck you have a 1 in 52 chance of picking it. Because there are 4 suits made up of 13 card each, you have a 13 in 52 chance of picking a particular suit. If you are looking for any of the kings, you have a 4 in 52 chance of picking a king because there are 4 kings in the deck. 4

Now after you pick the first card in the deck your chances now change unless you put the card back before picking again. If you pick a card and it is not the one you want and you keep it and pick another one, then your chance is now out of 51 instead of 52. If you are looking for the ace of diamonds from a full deck your chance is 1 in 52. If you pick a card and it is not the ace that you want, your chance is now 1 in 51. If you still didn’t find it and you don’t put your two cards back your chance is now 1 in 50. If you put the picked card back into the deck the chance stays 1 in 52. The number that you pick from will go down with every wrong pick and your chance of picking the right card will go up. 5

Let’s now look at chance in a very general way Let’s now look at chance in a very general way. We look at the total number of choices and the total number of possible desired outcomes and we make a fraction. Desired outcome Total number of choices Another example is, if you have a jar of candy with a couple of different colors and you just want one color, like red, the chance of picking that color would be. Number of Red candy Total number of candy 6

Now when you play a game, you should have a better understanding of what your chance is. In a game of chance the coin, spinner, die or cards don’t remember what you picked last and don’t think about what you will pick next. Every toss, spin or pick is an independent event, with a probability. So next time you play a game of chance think about your possible outcomes and your chances of winning!