Let's consider scenarios where we're drawing cards from multiple decks. To start, let's look at a single deck with one triangle card and two star cards. If you draw one card, it's more likely to be a star because there are more star cards available.
Now, let's draw one card each from two decks. We want to find which pair of cards is more likely to be drawn. Let's compare drawing a star and a two versus a triangle and a four. The first deck has one triangle and two stars, while the second deck has two twos and one four. There's only one way to draw a triangle and a four, but you could draw a star and a two four different ways.
So, drawing a star and a two is more likely because there are more ways to match the goal.
Next, let's compare drawing a triangle and a two versus a triangle and a four.
The first deck has one triangle, while the second deck has two twos and one four. There's only one way to draw a triangle and a four. But you could draw a triangle and a two two different ways.
So drawing a triangle and a two is more likely. We can see that a triangle and a two is the more likely goal when we lay out the possible combinations. There are more pairs that match a triangle and a two than a triangle and a four. Let's use this logic for another pair of goals.
Drawing a one and a two versus a star and a square. The first deck has one one and the second has two twos. So there are two ways to meet that goal. For the second goal, there are two stars in the first deck and two squares in the second. There are four ways to draw a star and a square. Since four is greater than two, drawing a star and a square is more likely.
We can also compare goals based on properties like even or odd numbers.
Let's see what's more likely. drawing a triangle and an even number or an odd number and a circle. There's one triangle in the first deck. In the second deck, all three cards have even numbers, so that's three possible ways.
For the other goal, the first deck has two odd-numbered cards, the one and the three. The second deck has one circle, so there are only two ways. Three is more than two, so getting a triangle and an even number is more likely.
