Let's calculate probabilities and compare likelihoods of different events.
Here we have two decks and we're drawing one card from each deck. The goal is to draw two odd cards. The total number of outcomes is the number of cards in the first deck multiplied by the number in the second. That's 2 * 3, which equals six. Next, let's see how many successful outcomes there are. For the first draw, we can pick a 1 or a three. For the second, we can pick a 1 or three. That gives us four pairs of successful outcomes. So the probability is four out of six or 4 six. Let's look at a different goal. What's the probability that we draw a white card that is smaller than a black card? We already found that there are six possible outcomes. Then there are two possible successful pairs. A white one and black two or a white one and black three. So the probability is 2 out of six or two.
Now, let's find which goal is more likely to be met for these decks. We found that the total number of outcomes is six and that the probability of drawing two odd cards is 4 sixths and the probability of drawing a white card that is less than a black card is 26ths.
So, drawing two odd cards has a higher probability.
Now, let's look at two different decks.
The white deck has the numbers 1 2 and two. The black deck has 1 2 and three.
The total number of outcomes is 3 * 3 which equals 9.
Our goal is to draw a white two and a black three. There are two white twos and one black three. So there are two ways we could meet the goal. The probability is 2 out of nine or 2 9ths.
What is the probability of drawing two cards that sum to four? We know there are nine possible outcomes. To sum to four, we would need to draw a white two and a black two or a white one and a black three. There are two white twos, so there are three successful outcomes in total. The probability is three out of nine.
Let's compare the probabilities of the last two goals. We found that the probability of drawing a white two and a black three from these decks is 2 out of 9. And the probability of drawing two cards that sum to four is three out of nine. 3 out of nine is larger. So this is the goal that is more likely to be met.
We calculated probabilities and then compared the likelihood of different events.
