Practice Questions on Geometric Distribution Formula

Question 1: A fair six-sided die is rolled repeatedly until a 6 is obtained. What is the probability that the first 6 occurs on the third roll?

Question 2: A student is studying for a biology exam. Each time the student takes a practice quiz, there is a 40% chance of getting a question correct. What is the probability that it takes the student at least 5 quizzes to get the first question correct?

Question 3: A factory produces light bulbs, and 8% of the bulbs are defective. What is the probability that the 10th bulb tested is the first defective one found?

Question 4: A basketball player makes free throws with a probability of 75%. What is the probability that it takes the player fewer than 4 attempts to make the first successful free throw?

Question 5: A fisherman catches fish at a certain spot with a probability of 20%. What is the probability that it takes the fisherman exactly 6 tries to catch the first fish?

Geometric Distribution is a probability distribution that tells the number of independent Bernoulli trials needed to achieve the first success. It is used to analyze situations where each trial has only two possible outcomes (success or failure), and the probability of success remains constant across all trials.