Let's practice comparing goals to see which is more likely. Here we're drawing one card and flipping a coin. The first goal is drawing an even number and flipping a heads. Since only the four is even, there's only one way to get an even number and heads. The second goal is drawing an odd number and a tails.
The one and five are odd. So there are two ways to get an odd number and a tails. Since two is more than one, drawing an odd number and getting tails is more likely.
Let's look at rolling two dice. The first goal is to roll an even number on the white dice and a number less than or equal to two on the black dice. The second goal is to roll an odd number on the white dice and a number greater than or equal to three on the black dice. The even numbers are 2, 4, and six. The odd numbers are 1, 3, and five. So the white dye has an equal number of successful outcomes for both goals. There are two ways the black dye could be less than or equal to two, one or two. There are four ways it could be greater than or equal to three. 3 4 5 or 6. So the second goal is more likely.
Here we have two decks and we're drawing one card from each. The first goal is a white card that's even and a black card with a triangle. All three white cards are even and there is one black card with a triangle. So there are three successful outcomes that match the first goal. The second goal is a white card with a star and a black card that is less than or equal to three. There are two white cards with stars and two black cards with numbers less than or equal to three, which gives us four possible successful pairs. Since four is greater than three, the second goal is more likely.
Here we have two different decks.
The first goal is to draw a white card with a two and a black card with a star.
There are three white twos and three black cards with stars. So, there are nine possible outcomes.
The second goal is to draw a white card that's even and a black card that's odd.
There are four even white cards and two odd black cards. So, there are eight possible outcomes for this goal. Nine is greater than eight. So, the first goal is more likely.
Next, let's compare drawing a card and rolling a dieice. The first goal is to draw a card with the number one and roll two or less on the die. There are two cards with a one and two die rolls that work. So, there are four total ways. For the second goal, we need to draw a card with a circle card and roll two or more on the die. There's only one circle card, but there are five die rolls that are two or more. So, there are five possible ways. Since five is greater than four, the second goal is more likely.
To find the likelier goal, we can count the different ways each goal can be achieved. The one with a larger amount of successful outcomes is more likely to happen.
