Question

When a certain glaze is applied to a ceramic surface, the probability is 11% that there will be discoloration, 16% that there will be a crack, and 22% 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. Let pX denote the success probability for X. Find pX .

Answer 1

The value of pₓ is 0.11.

Explanation:

The effects of a certain glaze on a ceramic surface are denoted as:

X = discoloration

Y = crack

Z = either discoloration or crack or both.

The success is denoted as 1 and failure as 0.

If X = 1 it implies that there is discoloration.

If X = 0 it implies that there is no discoloration.

The probability that there will be discoloration on applying a certain glaze is,

P (X = 1) = 0.11

Then the probability that there will be no discoloration is:

P (X = 0) = 1 - P (X = 1) = 1 - 0.11 = 0.89.

The variable pₓ denotes the success probability of random variable X.

In case of success the value of X is 1.

The probability of X = 1 is,

P (X = 1) = 0.11

Thus, the value of pₓ is 0.11.