2.111 (4 points) An art dealer receives a shipment of five old paintings from abroad, and, on the basis of past experience, she feels that the probabilities are, respectively, 0.76, 0.09, 0.02, 0.01, 0.02, and 0.10 that 0, 1, 2, 3, 4, or all 5 of them are forgeries. Since the cost of authentication is fairly high, she decides to select one of the five paintings – 2– MATH-4751/6751, Fall-2020 Homework #3 at random and send it away for authentication. If it turns out that this painting is a forgery, what probability should she now assign to the possibility that all the other paintings are also forgeries?

0.675675675 = 67.57%

Step-by-step explanation:

P(P₀) = 0.76

P(P₁) = 0.09

P(P₂) = 0.02

P(P₃) = 0.01

P(P₄) = 0.02

P(P₅) = 0.1

P(F) is the probability that the first painting is a forgery

P(F | P₀) = 0

P(F | P₁) = 0.2

P(F | P₂) = 0.4

P(F | P₃) = 0.6

P(F | P₄) = 0.8

P(F | P₅) = 1

P(P₅ | F) = [P(F | P₅) x P(P₅)] / {[P(F | P₁) x P(P₁)] + [P(F | P₂) x P(P₂)] + [P(F | P₃) x P(P₃)] + [P(F | P₄) x P(P₄)] + [P(F | P₅) x P(P₅)]}

P(P₅ | F) = (1 x 0.1) / [(0.2 x 0.09) + (0.4 x 0.02) + (0.6 x 0.01) + (0.8 x 0.02) + (1 x 0.1)] = 0.1 / (0.018 + 0.008 + 0.006 + 0.016 + 0.1) = 0.1 / 0.148 = 0.675675675 = 67.57%

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

good luck on ur quiz test or homework. have a good day : )