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 px denote the success probability for X. Find px.

b. Let py denote the success probability for Y. Find pY.

c. Let pz denote the success probability for Z. Find pz

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

e. Does pz=px+py?

f. Does Z = X + Y? Explain.

Answer:

Step 1 of 6:

(a)

In this question, we are asked to find the success probability for and hence .

Certain glaze is applied to a ceramic surface.

Discoloration in surface =

Crack in surface = 20%

There will be either discoloration or a crack, or both in surface = 23%

Let if there is a discoloration in surface, let otherwise.

Let if there is a crack in surface, let otherwise.

Let if there will be either discoloration or a crack, or both in surface, let otherwise.

Hence the success probability for () is .

Step 2 of 6:

(b)

In this question, we are asked to find the success probability for and hence .

Hence the success probability for () is .

Step 3 of 6:

(c)

In this question, we are asked to find the success probability for and hence .

Hence the success probability for () is .