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. Input your answers in the fractional form (do not simplify).

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

Step-by-step explanation:

Given

See attachment for proper format of table

--- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

In this row:

and

So, we have:

P(A) is then calculated as:

Solving (b): P(B)

Here, we only consider data in the Yes column.

In this column:

    and

So, we have:

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.

This cell is: [Supplier 1][Yes]

And it is represented with; n(A n B)

So, we have:

The probability is then calculated as:

Solving (d): P(A u B)

This is calculated as:

This gives:

Take LCM

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a