1. What is Nth Term Probability?

The nth term probability calculates the chance of exactly k successes in n independent trials, each with success probability p. This is known as the binomial probability distribution.

2. How Does the Calculator Work?

The calculator uses the binomial probability formula:

Where:

• \( n \) — Number of trials
• \( k \) — Number of successes
• \( p \) — Probability of success on a single trial
• \( \binom{n}{k} \) — Binomial coefficient ("n choose k")

Explanation: The formula accounts for all possible ways k successes can occur in n trials, weighted by the probability of each specific sequence.

3. Importance of Probability Calculation

Details: Binomial probability is fundamental in statistics, used in quality control, medical testing, risk assessment, and many other fields requiring probability analysis of independent events.

4. Using the Calculator

Tips: Enter number of trials (n ≥ 1), number of successes (0 ≤ k ≤ n), and probability (0 ≤ p ≤ 1). All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between binomial and other distributions?
A: Binomial is for discrete yes/no outcomes with fixed trials and constant probability, unlike Poisson (for rare events) or Normal (continuous).

Q2: When is binomial probability appropriate?
A: When trials are independent, probability is constant, and there are only two possible outcomes per trial.

Q3: What if I need cumulative probability?
A: This calculates exact probability. For "k or more" or "k or less" you'd need to sum multiple probabilities.

Q4: Are there limitations to binomial probability?
A: It assumes independence between trials and constant probability. For dependent events, other models are needed.

Q5: How accurate is this calculator?
A: Very accurate for n up to about 1000. For very large n, normal approximation may be better.