Categorical distribution is a type of probability distribution that involves a set of possible categories or outcomes. It is often used to model the probability of an outcome occurring within a certain category. For example, if we were to toss a coin, the possible outcomes would be heads or tails, and the probability of each outcome occurring would be 0.5.

To better understand categorical distribution, let’s take a look at a few examples.

Example 1:

Suppose we have a bag containing 10 red marbles and 20 blue marbles. If we were to randomly select a marble from the bag, what is the probability that the selected marble is red?

In this example, the possible outcomes are red or blue, and the probability of each outcome occurring is 0.33. This is because there are 10 red marbles and 20 blue marbles in the bag, giving us a total of 30 marbles. Since the probability of an outcome occurring is determined by the number of outcomes divided by the total number of possibilities, the probability of a red marble being selected is 10/30 = 0.33.

Example 2:

Suppose we have a deck of cards containing 52 cards. If we were to randomly select a card from the deck, what is the probability that the selected card is a red card?

In this example, the possible outcomes are red or black, and the probability of each outcome occurring is 0.5. This is because there are 26 red cards and 26 black cards in the deck, giving us a total of 52 cards. Since the probability of an outcome occurring is determined by the number of outcomes divided by the total number of possibilities, the probability of a red card being selected is 26/52 = 0.5.

Example 3:

Suppose we have a bag containing 10 red balls, 20 blue balls, and 30 green balls. If we were to randomly select a ball from the bag, what is the probability that the selected ball is red, blue, or green?

In this example, the possible outcomes are red, blue, or green, and the probability of each outcome occurring is 1. This is because there are 10 red balls, 20 blue balls, and 30 green balls in the bag, giving us a total of 60 balls. Since the probability of an outcome occurring is determined by the number of outcomes divided by the total number of possibilities, the probability of a red, blue, or green ball being selected is 1.

In summary, categorical distribution is a type of probability distribution that involves a set of possible categories or outcomes. It is often used to model the probability of an outcome occurring within a certain category. By understanding the possible outcomes and their corresponding probabilities, we can better understand the likelihood of an event occurring.