Bernoulli distribution is a special case of the Binomial distribution when which parameter equals 1?

• A. n = 1
• B. p = 0.5
• C. k = 1
• D. lambda = 1

Answer: (A)

The key idea is that Bernoulli describes a single trial with two outcomes, typically labeled success or failure. The Binomial distribution counts the number of successes in a fixed number of independent Bernoulli trials with the same probability of success p. If you have only one trial, the number of successes can be either 0 or 1, with probabilities P(X=1)=p and P(X=0)=1-p. That is exactly the Bernoulli(p) distribution. So Bernoulli is the special case of Binomial when the number of trials is one. The other options don’t establish this equivalence: p being 0.5 is just a particular probability, not what collapses Binomial to Bernoulli, and lambda relates to Poisson, not Bernoulli/Binomial.