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brooklynunderwood46
21.09.2020 •
Mathematics
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows:
Edge Finish
Excellent Good
Surface Excellent 80 2
Finish Good 10 8
Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. If a part 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)
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Ответ:
Step-by-step explanation:
From the question:
The given table is as follows:
Edge Finish
Excellent Good
Surface Excellent 80 2
Finish Good 10 8
So, we are being told that,
A represent the event that a sample has an excellent surface finish, and let B denote the event that a sample has excellent edge finish
The objective is to fin the following probabilities
P(A)
A = (80 +2) = 82
The total samples of cast = 80 + 10 +2 + 8 = 100
∴ P(A) = 82/100
P(A) = 0.82
P(B)
B = 80+10
B = 90
P(B) = 90/100
P(B) = 0.90
c) P(A')
(A') are the sets that are not in A but they are in the samples
i,e
(A') = 100 - 82
(A') = 18
So;
P(A') = 100/18
P(A') = 5.56
d) P(A ∩ B)
A = ( 80, 2)
B = (80,10)
The intersection of A and B (i.e. A ∩ B) is the common value between them which is 80
P(A ∩ B) = 80/100
P(A ∩ B) = 0.80
e) P(A ∪ B)
A = ( 80, 2)
B = (80,10)
The union of A and B is the addition of A and B
i.e. 80+2+10 = 92
P(A ∪ B) = 92/100
P(A ∪ B) = 0.92
f. P(A' ∪ B)
A' = (10, 8)
B = (80,10)
The union of A complement and B is
(A' ∪ B) = 10 + 8 + 80
(A' ∪ B) = 98
P(A' ∪ B) = 98/100
P(A' ∪ B) = 0.98
Ответ:
5 + n - 5 = 10 - 10
Step-by-step explanation: