When a certain glaze is applied to a ceramic surface, the

QUESTION:

When a certain glaze is applied to a ceramic surface, the probability is 5% that there will be discoloration, 20% that there will be a crack, and 23% that there will be either discoloration or a crack, or both. Let X = 1 if there is discoloration, and let X = 0 otherwise. Let Y = 1 if there is a crack, and let Y = 0 otherwise. Let Z = 1 if there is either discoloration or a crack, or both, and let Z = 0 otherwise.

a. Let \(p_{X}\) denote the success probability for \(X\). Find \(p_{X}\).

b. Let \(p_{Y}\) denote the success probability for \(Y\). Find \(p_{Y}\).

c. Let \(p_{Z}\) denote the success probability for \(Z\). Find \(p_{Z}\).

d. Is it possible for both \(X\) and \(Y\) to equal 1?

e. Does \(p_{Z}=p_{X}+p_{Y}\)?

f. Does Z = X + Y ? Explain.

Equation Transcription:

Text Transcription:

p_X

X

p_Y

Y

p_Z

Z

p_Z = p_X + p_Y