Chat with our AI personalities
p=a+b+c for a
Let P = { x0, x1, x2, ..., xn} be a partition of the closed interval [a, b] and f a bounded function defined on that interval. Then: * the upper sum of fwith respect to the partition P is defined as: U(f, P) = cj (xj - xj-1) where cj is the supremum of f(x)in the interval [xj-1, xj]. * the lower sum of f with respect to the partition P is defined as L(f, P) = dj (xj - xj-1) where dj is the infimum of f(x) in the interval [xj-1, xj].
There are symbols missing from your question which I cam struggling to guess and re-insert. p(a) = 2/3 p(b ??? a) = 1/2 p(a ∪ b) = 4/5 p(b) = ? Why use the set notation of Union on the third given probability whereas the second probability has something missing but the "sets" are in the other order, and the order wouldn't matter in sets. There are two possibilities: 1) The second probability is: p(b ∩ a) = p(a ∩ b) = 1/2 → p(a) + p(b) = p(a ∪ b) + p(a ∩ b) → p(b) = p(a ∪ b) + p(a ∩ b) - p(a) = 4/5 + 1/2 - 2/3 = 24/30 + 15/30 - 20/30 = 19/30 2) The second and third probabilities are probabilities of "given that", ie: p(b|a) = 1/2 p(a|b) = 4/5 → Use Bayes theorem: p(b)p(a|b) = p(a)p(b|a) → p(b) = (p(a)p(b|a))/p(a|b) = (2/3 × 1/2) / (4/5) = 2/3 × 1/2 × 5/4 = 5/12
31
One tenth (1/10) = 10%. Think of Percent as 'per hundred', so to find a percentage, do this: F = P% = P/100, where F is the fraction, and P is the percentage.You are given F, so solve for P. Rearrange and you have P = 100 x F, so we have P = [100 x (1/10)] = 10.