Question 1

What is the difference between independent and dependent probability?

Accepted Answer

Events are independent if the outcome of one does not affect the other (e.g., rolling two dice, P(A∩B) = P(A)×P(B)). Dependent events affect subsequent likelihoods (e.g., drawing cards without replacement).

Question 2

What is the Binomial Probability formula?

Accepted Answer

P(X=k) = (n choose k) × p^k × (1-p)^(n-k), modeling exactly k successes across n independent Bernoulli trials with success probability p.

Question 3

How do permutations differ from combinations in probability?

Accepted Answer

Permutations nPr = n! / (n-r)! count arrangements where order matters. Combinations nCr = n! / (r!(n-r)!) count groups where order is irrelevant.

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