Statistics
Class 12

Binomial Probability Distribution

P(X=r)=(nr)pr(1p)nrP(X=r) = \binom{n}{r} p^r (1-p)^{n-r}
0246810976.5624999999993μ976.5624999999995μ976.5624999999998μ976.5625μ
P(X=r) = C(n,r) × pʳ × (1-p)^(n-r)

Adjust Variables

Trials n
n =
120
Probability p
p =
0.10.9

Probability of exactly r successes in n independent trials with success probability p.

Real-World Applications

Quality control — P(k defectives in sample of n).

Medicine — P(k patients respond to treatment).

Genetics — P(k offspring with trait).

Polling — P(k people support candidate in sample).

Sports — P(k hits in n at-bats).

Insurance — P(k claims in n policies).

Manufacturing — P(k machines failing in plant).

Epidemiology — P(k infections in population).

Finance — P(k profitable trades in series).

Education — P(k students passing exam).

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