Binomial Distributions
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
+2
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a binomial distribution?
Back
A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent outcomes under a given set of parameters.
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
2.
FLASHCARD QUESTION
Front
What are the key characteristics of a binomial experiment?
Back
1. The number of trials (n) is fixed. 2. Each trial has only two possible outcomes (success or failure). 3. The trials are independent. 4. The probability of success (p) is the same for each trial.
3.
FLASHCARD QUESTION
Front
What is the formula for calculating the probability of exactly k successes in a binomial distribution?
Back
P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!)
Tags
CCSS.HSS.MD.A.3
CCSS.HSS.MD.A.4
4.
FLASHCARD QUESTION
Front
How do you calculate the mean of a binomial distribution?
Back
Mean (μ) = n * p, where n is the number of trials and p is the probability of success.
5.
FLASHCARD QUESTION
Front
How do you calculate the variance of a binomial distribution?
Back
Variance (σ²) = n * p * (1 - p), where n is the number of trials and p is the probability of success.
6.
FLASHCARD QUESTION
Front
What is the probability of getting at least k successes in a binomial distribution?
Back
P(X ≥ k) = 1 - P(X < k) = 1 - Σ P(X = i) for i = 0 to k-1.
7.
FLASHCARD QUESTION
Front
What does it mean for trials to be independent in a binomial experiment?
Back
It means the outcome of one trial does not affect the outcome of another trial.
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