Let's explore how to figure out possibilities and calculate probability.
We'll start with a single deck of three cards. The first question asks for the total number of possible outcomes. Since there are three different cards in the deck, there are three possible outcomes when drawing one card.
Now, let's set a goal. Our goal is to draw a card with a star on it. How many outcomes would meet this goal? Looking at the three cards, two of them have a star. So there are two successful outcomes. With that information, we can calculate the probability of hitting our goal. There are two cards with stars and three possible cards. So the probability is 2 out of three or 2/3.
The probability that a goal is met is the number of successful outcomes divided by the total number of outcomes.
We calculated that there were three total outcomes and two successful outcomes. So our probability is 2/3.
Let's try this with a second deck. We're going to draw one card from each deck.
And each deck has three cards. To find the total number of combinations, we multiply the possibilities. Three from the first deck times three from the second gives us nine total possible outcomes.
Now, let's set a new goal. Drawing a star card from the first deck and a two from the second deck. How many outcomes meet this goal? The first deck has two cards with stars and the second deck also has two cards with the number two.
To find the number of ways we can get a star from the first deck and a two from the second, we multiply the number of successful options for each. That's two from the first deck times two from the second, which equals four successful outcomes.
So, what's the probability of hitting the goal of drawing one star and one two? We need to divide the number of successful outcomes by the total number of outcomes. There are four ways to successfully draw one star and one two and nine total possible outcomes. So the probability of drawing one star and one two is 4 / 9 or 4 9ths.
When each possibility is equally likely, you can find the probability by dividing the number of successful outcomes by the total number of possible outcomes.
