Our lives are full of random events that we can’t control. Rolling a pair of dice, tossing a coin, or conducting a raffle are all examples of common, random events. As young math students who have already started learning about probability know, there are many different types of events, and knowing how they interact with one another can give us an edge when we are trying to predict the outcome of such events.
The Importance of Probability
If we speak generally, we can say that the probability of an event occurring is the number of ways it can happen, divided by the total number of possible outcomes. If we have a regular 6-sided die and we throw it, the probability of it landing on a particular number, let’s say 5, is the number of possible outcomes (1, because only one side has a 5 on it) divided by the total number of outcomes (6, because the die has 6 sides). Therefore, we know the probability of rolling a 5 is ⅙.
Of course, we could roll the die 100 times and never see a 5. This is unlikely, but not impossible, and it serves as a good reminder that probability is just a guide, not a guarantee.
Different Types of Events
As we mentioned, tossing a coin, rolling a die, and conducting a raffle are all examples of random events. Different events can have different characteristics, even the number of outcomes. An event can be getting a head when you toss a coin. Similarly, choosing a heart from a deck of cards is an event, even though there are 13 possible hearts to choose from in the deck.
Now that we know events can be one outcome or include several outcomes, let’s take a closer look at three different types of events that students will need to deal with in their 6th grade classroom. These three types of events are independent events, dependent events, and mutually exclusive events.
Independent events are those that are not affected by any other events taking place. Tossing a coin is an example of an independent event. The coin is simply a coin, it can’t remember what happened the last time it was tossed, and therefore each time it is tossed is an isolated action. A coin could be tossed 99 times in a row and if all 99 had come out as heads, the probability of the following toss coming out as heads would still be 50/50. Believing that a tail “is due” is false, and this is known as the Gambler’s Fallacy.
Dependent events, as you may have guessed, are events that can be affected by other events. Let’s take our example of drawing a heart from a deck of playing cards again. If we try this, regardless of what the first card we draw is, we have impacted our next attempt because the deck of cards will have one less card in it.
On our first attempt, our odds are 13/52, since there are 13 hearts in a 52-card deck. If we draw a heart, and we attempt to draw another one on our second attempt, our odds have changed from the original 13/52 odds we had for the first attempt, to 12/51. If we do not draw a heart at first, our odds the second time are 13/51.
If we were to draw our first card and see it is not a heart, then proceed to return it to the deck, our odds have not changed. This is known as a replacement.
Mutually Exclusive Events
Finally, we must get to know mutually exclusive events. If two events are mutually exclusive, we cannot get both events at the same time. It is a case of one or the other, but never both.
Getting both a head and a tail from a single toss of a coin is an example of mutually exclusive events because we can never get both results from just one toss. Another example would be drawing both an ace and a king when drawing one single card from a deck. On the other hand, drawing a king and drawing a heart are not mutually exclusive events, as there is one king of hearts in the deck that satisfies both characteristics.
Improve Your Child’s Chances with OMC
Whatever your experience with odds, it’s probable that you’ve learned something from this article. If you want your child to continue learning at an unmatched rate, contact OMC and enroll your young learner in any number of courses covering each and every grade, 1-1 classes to plug gaps in your child’s knowledge, and special preparation classes for tests that mimic exam environments so your child can stay stress and panic-free when the day of finals arrives.
Contact OMC today to give your child the best math tutoring available!