The hypergeometric distribution is a type of discrete distribution that represents the probability of the number of successes achieved on performing ‘n’ number of trials of a particular experiment provided that there is no replacement. The binomial distribution is the closest approximation of hypergeometric distribution if the sample size chosen is 5% or less of the total population. The only difference between a binomial distribution and hypergeometric distribution is that the events are independent in the case of the binomial distribution, while the trials depend on each other in the case of the hypergeometric distribution. Two key aspects to keep in mind while applying hypergeometric distribution to a set of data is that the size of the population is finite, and the trials of the experiments are performed without replacement.
Examples of Hypergeometric Distribution
1. Poker
Suppose you have a fair deck of playing cards, and you are supposed to draw five cards at a time. The probability that all the cards that are drawn are spades can be calculated easily with the help of hypergeometric distribution. It must be noted that the binomial distribution cannot be applied here because the cards are drawn without replacement, which means that the probability of success of the experiment changes with each draw.
2. Number of Voters
Suppose that a district consists of 100 female voters and 200 male voters. If a group of ten voters is selected at random, then the probability that eight of the selected voters would be male can be calculated with the help of hypergeometric probability distribution.
3. Candy Box
Suppose you have a candy box that consists of ten candies, six of them are sweet, while four of them are sour in taste. When you tend to randomly pick four candies out of the box, the probability that three of them are sweet and one is sour in taste can be calculated easily with the help of a geometric distribution function.
4. Forming a Committee at an Educational Organization
Suppose an educational organisation such as a school or college needs a mixed group of teachers, students, lab assistants, and principals to organize an annual function. Let us say twenty people are selected randomly out of a total population of 60 teachers, 100 students, 30 lab assistants, and 10 principals. The probability that the newly formed committee would have 2 teachers, 4 students, 3 lab assistants, and 1 principal can be calculated easily with the help of geometric probability distribution.
5. A Box full of Colourful Balls
Suppose a box contains ten green balls, twenty red balls, ten yellow balls, and five white balls. Let us say ten balls are randomly drawn from the box, the probability that three balls would be blue in colour can be calculated with the help of hypergeometric probability distribution. Likewise, the probability that four of them would be yellow in colour, two would be white in colour, two would be red coloured, etc., can be determined in a similar manner.
6. Rolling Multiple Dies
One of the prominent examples of a hypergeometric distribution is rolling multiple dies at the same time. Suppose six dies are rolled simultaneously, then the probability that four of the dies would have an even number on their top face, while two dies would have an odd number on the top, can be estimated with the help of hypergeometric distribution.
7. Number of Defective Products in a Consignment
Suppose a shoe industry is assigned to make 200 pairs of sneakers. When the consignment is packed, ten shoe boxes are selected randomly to look for faults and defects. It is required to calculate the probability that six of the ten pairs of shoes would be defective. The probability distribution best suited in such a case is the hypergeometric distribution.
8. Students Belonging to Different Disciplines
Suppose the total strength of students in a school is equal to 2000. A hundred students are selected at random to form a social service organisation. The probability that 50 of the chosen students belong to the science department, 20 come from arts and humanities discipline, and the rest 30 belong to commerce is required to be calculated. The total students participating in the experiment and the size of the chosen sample are finite in nature, and the replacement of samples is avoided, hence the hypergeometric probability distribution is the most preferred in such a case.
9. Mobile Phone Repair Shop
Let us say that a mobile phone repair shop receives a total number of twenty mobile phones to be repaired on a daily basis. Suppose, the next day, the owner of the repair shop randomly selects ten mobile phones and gives them to the technician. The probability that six of the selected mobile phones would have a hardware problem, while four of them would be having a software-based problem, is calculated with the help of hypergeometric probability distribution. This helps the shop owner keep the spare parts handy in case a replacement of the components in the internal circuitry of the mobile phone is required.
10. Getting Hired for an Internship
The hypergeometric probability distribution function can be effectively used to determine your chances of being selected for a particular internship. Suppose a total of 25 people register themselves for the internship program. The probability that the first twenty applications get selected for the personal interview can be calculated with the help of hypergeometric probability distribution. Also, the likeliness of ten applicants qualifying the personal interview out of the twenty selected applicants can be represented in a similar manner with the help of hypergeometric distribution.
11. Mahjong
Mahjong is a card game that has Chinese origins. It consists of a total of 112 cards. 108 cards of the total cards are arranged in such a way that they are numbered one to nine, each card has four copies, and there are three such sets of cards. In addition, there are four Zhong cards marked with a red block. The person at the end possessing at least three Zhong cards is declared the winner of the game. The hypergeometric probability distribution is best suited and prominently used in such a case to calculate the chances of a person winning the game.
