Hypergeometric Distribution: 동영상 및 연습문제

A shipment contains $7,500$ bolts, with $18\%$ classified as substandard. If a supervisor randomly selects $6$ bolts for testing, what is the probability that none of the selected bolts are substandard? Selections are made without replacement.

A box contains $10$ light bulbs, of which $4$ are defective and $6$ are good. If $3$ bulbs are randomly selected from the box, what is the probability that exactly one is defective?

A box contains $10$ light bulbs, of which $4$ are defective and $6$ are good. If $2$ bulbs are randomly selected from the box, what is the probability that exactly $1$ is good and $1$ is defective?

In a class of $20$ students, $7$ students scored above the threshold on a test. Three students are chosen at random without order. What is the probability that exactly two of the chosen students scored above the threshold?

A design team has $6$ engineers and $4$ designers. Two team members are chosen at random for a site visit. What is the probability that the pair contains one engineer and one designer?

A class has $20$ students, of whom $6$ earned an A on a test. Three students are selected at random without replacement and called in order. What is the probability exactly two of the first three called earned an A? Is this outcome unusual at the $0.05$ level?

A mixtape contains $10$ tracks and you enjoy $3$ of them. The player shuffles and plays each track once in a random order. What is the probability that the first two tracks played are both ones you enjoy? Is this outcome unusual at the $0.05$ significance level?

A hardware kit contains $40$ bolts: $25$ stainless, $10$ brass, and $5$ aluminum. Two bolts are chosen at random without replacement. What is the probability that both are stainless? Give your answer as a simplified fraction.

Four cards are drawn at random without replacement from a standard $52$-card deck. What is the probability that all four cards are from the same suit?

A sweepstakes involves picking $4$ numbers from an urn containing balls numbered $1\text{–}28$. Four balls are drawn at random, without replacement. If a participant's chosen set of four numbers matches all those drawn (order does not matter), what is the probability of winning with one entry?

A classroom has $40$ students, $6$ of whom are left-handed. Four students are chosen at random without replacement, and the number of left-handed students among the chosen four is recorded. Is this a binomial experiment? Select the best answer.

A sample of $22$ students includes $8$ who play violin and $14$ who do not. Two students are picked at random without replacement. What is the probability that both chosen students play violin?

A quality control inspector has a lot containing $12$ gadgets, with exactly $1$ defective. She selects $4$ gadgets at random without replacement and will pass the lot only if none of the selected gadgets are defective. What is the probability that the lot will be passed?

A panel of $4$ is chosen at random from $15$ male and $10$ female applicants. What is the probability that exactly $2$ of the selected are female?

A club has $30$ undergraduate members and $20$ graduate members. A committee of $4$ is selected uniformly at random. What is the probability that all selected members are graduate students?

A researcher selects a random sample of $15$ university students and records each student's final exam score as a number out of $100$. Is this a binomial experiment?

A student answers a quiz containing exactly $12$ independent multiple-choice questions, each with one correct answer. The number of correct answers is recorded. Is this a binomial experiment? Select the best answer.

A researcher randomly selects $50$ households in a large city and records whether each household owns at least one electric vehicle. Is this a binomial experiment? Select the best answer.

A shipment contains $80$ laptops, of which $5$ are defective (unknown to the inspector). The inspector randomly tests $4$ laptops without replacement. The shipment is accepted only if none of the $4$ tested laptops is defective. What is the probability of accepting the shipment?

A hiring panel selects $6$ applicants at random from a pool of $10$ male and $12$ female candidates. What is the probability that the selected group contains exactly $2$ males and $4$ females?

In a raffle, $5$ winning tickets are drawn without replacement from a pool of $40$ tickets. A player buys $5$ distinct tickets. What is the probability that exactly $3$ of the player's tickets are winners?