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Sum of binomial probabilities P(X = 0) + P(X = 1) + … + P(X = n) equals
A0
B1
Cn
Dnp
Answer & Solution
Correct answer: B. 1
1. The total probability over all possible outcomes is 1 by definition.
2. For Bin(n, p): ΣP(X = k) for k = 0…n = (p + q)ⁿ = 1ⁿ = 1.
3. Holds for every probability distribution.
4. Hence (B) is correct.
_Source: Maharashtra Balbharati Std XII Mathematics & Statistics (Commerce), Ch 8 "Probability Distributions", §8.1 ¶§8.1_
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