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