Explain the following concepts in probability and provide examples for each: 1. Independent vs Dependent Events 2. Mutually-exclusive Events 3. Conditional Probability. In classical probability, can the probabi
True or false. If A and B are 2 independent events, the probability of A given B must equal the probability of A . Events A and B are mutually exclusive. P (A) = 0.25 and P (B) = 0.18. What is the probability that neither A nor B will occur?
Explain the following concepts in probability and provide examples for each: 1. Independent vs Dependent Events 2. Mutually-exclusive Events 3. Conditional Probability. The probability of A or B is 0.8 , i.e, P ( A or B ) = P(A \cup B) = 0.8 . The probability of B is 0.3 . Wha...
3. Mutually Exclusive vs. Independent Events It’s vital not to confuse “mutually exclusive” with “independent” events. Two events are independent if the occurrence of one event does not affect the probability of the other event happening. Mutually exclusive events are always dependent because ...
‣ Mathematically: If events A and B areindependent, P(A and B) = P(A) × P(B). Then, probability trees bayesian inference posterior ‣ The probability we just calculated isalso called the posterior probability. P(H1: good die on the Right | you rolled ≥4 with thedie on the Ri...
1.5. Multiplication rule for independent events If two events A and B are independent (the occurrence of one does not affect the occurrence of the other), the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B) 2. Formulas ...
‣ Mathematically: If events A and B areindependent, P(A and B) = P(A) × P(B). Then, probability trees bayesian inference posterior ‣ The probability we just calculated isalso called the posterior probability. P(H1: good die on the Right | you rolled ≥4 with thedie on the Ri...
Because we replace and re-shuffle, the draws are independent, so the AND means multiply. P(win in two draws) =(3/4)*(1/4) = 3/16 P(win in two or fewer draws) = P(win in one draw) + P(win in two draws) = 1/4 + 3/16 = 7/16 P(at least three draws to win) = 1...
For example, in an ‘all models are wrong’ context there is no need for theta (models) to come with mutually exclusive, sum to one structure. Bayesians seem to like to call this sort of case ‘M-open’. To a frequentist, (or likelihoodist or other) a pvalue and related quantities...
Example 7 A set of dependent random variables such that any of its subsets consists of mutually independent variables Let n⩾3 and A be the set of all (n-1)-dimensional vectors a=(a1,…,an-1), where ai=1 or 0, i=1,…,n-1. Then the set A contains 2n-1 elements, i.e. th...