Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows: conforms
yes no
1 22 8
supplier 2 25 5
3 30 10

Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample from any supplier conforms to specifications. If a disk is selected at random, determine the following probabilities.

a. P(A)=0.3
b. P(B)=0.77
c. P(A ∩ B) =0.22
d. P(A U B)=0.85

Answer

Explanation:

Given

See attachment for proper data presentation

--- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

and

P(A) is then calculated as:

Solving (b): P(B)

We only consider data in the Yes column.

Here:

    and

P(B) is then calculated as:

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

i.e. [Supplier 1][Yes]

This is represented as: n(A n B)

The probability is then calculated as:

Solving (d): P(A u B)

This is calculated as:

This gives:

Take LCM