📊 Binomial Distribution Visualizer - Probability
ProbabilityWhat's happening? P(X=k) = C(n,k)p^k(1-p)^(n-k). The distribution peaks at the mean μ = np. Change p to skew the distribution left or right.
Probability: 3-5 questions every year.
JEE tests binomial, conditional probability, expected value.
Key formulas
Binomial Distribution Formulas
Binomial
P(X=k) = C(n,k) p^k (1-p)^(n-k)
n trials, k successes
Mean
E(X) = np
Expected value
Variance
Var(X) = np(1-p)
SD = sqrt(np(1-p))
Conditional
P(A|B) = P(A and B)/P(B)
Given B occurred
Step-by-step problem solving
How to solve maths problems in JEE
- Check binomial conditions
- Identify n, k, p
- Apply P(X=k) = C(n,k)p^k(1-p)^(n-k)
- Cumulative: sum probabilities
Common JEE mistakes
What students get wrong
Not checking conditions
Fixed n, independent, 2 outcomes, constant p
Combinations
C(n,k) = n!/(k!(n-k)!)
Mean vs variance
Mean = np, Variance = np(1-p)
Approximation conditions
Poisson: np<10. Normal: np>5, n(1-p)>5
FAQs
Binomial Distribution Questions
When binomial?
Fixed n, independent, 2 outcomes, constant p
P(X<=k)?
Sum P(X=0) + ... + P(X=k)
Mean and variance?
Mean = np, Var = np(1-p)
Poisson approximation?
n large, p small, np finite