ProbabilityEvents

Samples of emissions from three suppliers are classi-
fied for conformance to air-quality specifications. The results
from 100 samples are summarized as follows:

Let $$A$$ denote the event that a sample is from supplier 1 , and let
$$B$$ denote the event that a sample conforms to specifications.
Determine the number of samples in $$A^{\prime} \cap B, B^{\prime},$$ and $$A \cup B$$ .

$$$n=100$$

$$A \rightarrow$$ from (1)

B $$\rightarrow$$ Samples that conferms To specicication

$$ A^{\prime} \cap B$$

$$B^{\prime}, A \cup B$$

$$A^{\prime } \cap B=25+30=55$$

$$B^{\prime}=8+5+10=23$$

$$A \cup B=8+22+25+30=85$$

Three events are shown on the Venn diagram in the
following figure:

Reproduce the figure and shade the region that corresponds to
each of the following events.

(a) $$A^{\prime} \quad$$ (b) $$(A \cap B) \cup\left(A \cap B^{\prime}\right)$$
(c) $$(A \cap B) \cup C \quad$$ (d) $$(B \cup C)^{\prime}$$
(e) $$(A \cap B)^{\prime} \cup C$$

a) $$A^{\prime}$$

b) $$(A \cap B) \cup(A \cap B^{\prime})$$

A

c) $$(A \cap B) \cup C$$

d) $$(B \cup C)^{\prime}$$

e) $$(A \cap B)^{\prime} \cup C$$