Question

Samples of emissions from three suppliers are classified 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. If a sample is selected at random, determine the following probabilities:

 (a) P(A) (b) P(B) (c) P(A (d) P(A∩B) (e) P(A∪B) (f)P(A'∩B)

Answer 1

answer:

given data,

the summarized of the results is 100 samples

the supplier 's is 1,2,3.

the conforms of the yes is 20,25,30.

the conforms of the no is 10,5,10.

• the randomly selected is determines is below, follows below.

a) the probability of P(A) IS

P(A)

(20+10)/100

( 30 )/100

0.30

0.30

b) the probability of P(B) IS

P(B)

(20+25+30)/100

(75)/100

0.75

0.75

c) the probability of P(A') IS

P(A')

1 - P(A)

1 - 0.30

0.70

0.70

d) the probability of P( A\cap B ) IS

P(A \cap B)

20/100

0.20

0.20

e) the probability of P( A U B ) IS

P(A U B)

P(A) + P(B) - P(A \cap B)

0.30 + 0.75 - 0.20

0.30+0.55

0.85

0.85

f) the probability of P( A'\cap B ) IS

P(A' \cap B)

(25+30)/100

(55)/100

0.55

0.55

NOTE: SO FINALLY THESE ARE THE ALL PROBABILITY'S OF THE GIVEN INFORMATION