AP Statistics Flashcards: The Geometric Distribution
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What does the geometric probability function calculate?
The geometric probability function calculates the probability that the first success in a sequence of independent trials occurs on a specific trial, x.
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What does the geometric probability function calculate?
The geometric probability function calculates the probability that the first success in a sequence of independent trials occurs on a specific trial, x.
What is a critical aspect of interpreting results from a geometric distribution?
Probabilities and parameters for a geometric distribution must always be interpreted in the context of the specific real-world scenario.
What are the two primary parameters of a geometric distribution that can be calculated?
The two primary parameters to calculate for a geometric distribution are its mean (1/p) and its standard deviation (sqrt(1-p)/p).
In a game where you roll a die until you get a 6 (p=1/6), how would you interpret the mean?
The mean is 1/(1/6) = 6. This means we would expect, on average, to roll the die 6 times to get the first 6.
What is the fundamental skill associated with the geometric probability function?
The fundamental skill is the ability to calculate the probability that the first success occurs on a specific trial number.
A basketball player has a 70% free-throw success rate (p=0.7). Calculate the standard deviation for the number of attempts until her first successful shot.
The standard deviation is sqrt(1-0.7)/0.7, which is approximately 0.65 attempts.
What does 'first success' signify in the context of a geometric random variable?
It signifies the specific outcome of interest occurring for the very first time in a sequence of trials.
How do you calculate the standard deviation of a geometric distribution?
The standard deviation of a geometric random variable is calculated with the formula sqrt(1-p)/p, where p is the probability of success.
If the probability of a defective chip is 0.05, what is the expected number of chips you would test to find the first defective one?
The expected number is the mean of the geometric distribution, which is 1/p = 1/0.05 = 20 chips.
What is a geometric random variable?
A geometric random variable gives the trial number on which the first success occurs in a sequence of independent trials.
How do you calculate the mean of a geometric distribution?
The mean of a geometric random variable is calculated using the formula 1/p, where p is the probability of success on any given trial.