Respuesta :
Answer:
[tex]P(A'\cup B)=\frac{84}{100}[/tex]
Step-by-step explanation:
Let A and B represents the following events.
A denote the event that a disk has high shock resistance.
B denote the event that a disk has high scratch resistance.
Given probabilities:
[tex]P(A)=\frac{70+16}{100}=\frac{86}{100}[/tex]
[tex]P(B)=\frac{70+9}{100}=\frac{79}{100}[/tex]
[tex]P(A')=\frac{9+5}{100}=\frac{7}{50}[/tex]
[tex]P(A\cup B)=\frac{70+16+9}{100}=\frac{95}{100}[/tex]
The probability of intersection of A and B is,
[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
Substitute the above values.
[tex]P(A\cap B)=\frac{86}{100}+\frac{79}{100}-\frac{95}{100}=\frac{70}{100}[/tex]
The probability of union of A' and B is,
[tex]P(A'\cup B)=P(A')+P(A\cap B)[/tex]
Substitute the above values.
[tex]P(A'\cup B)=\frac{7}{50}+\frac{70}{100}[/tex]
[tex]P(A'\cup B)=\frac{14}{100}+\frac{70}{100}[/tex]
[tex]P(A'\cup B)=\frac{84}{100}[/tex]
Therefore, [tex]P(A'\cup B)=\frac{84}{100}[/tex].
Using Venn probabilities, it is found that the desired probability is given by:
[tex]P(A' \cup B) = \frac{21}{25}[/tex]
The or probability of Venn sets is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this problem, we want:
[tex]P(A' \cup B) = P(A') + P(B) - P(A' \cap B)[/tex]
We have that:
[tex]P(A') = \frac{7}{50}[/tex]
[tex]P(B) = \frac{79}{100}[/tex]
[tex]P(A' \cap B)[/tex] is probability of A not happening and B happening, thus low shock resistance and high scratch resistance, thus [tex]P(A' \cap B) = \frac{9}{100}[/tex]
Then
[tex]P(A' \cup B) = P(A') + P(B) - P(A' \cap B)[/tex]
[tex]P(A' \cup B) = \frac{7}{50} + \frac{79}{100} - \frac{9}{100}[/tex]
[tex]P(A' \cup B) = \frac{14}{100} + \frac{70}{100}[/tex]
[tex]P(A' \cup B) = \frac{84}{100}[/tex]
[tex]P(A' \cup B) = \frac{21}{25}[/tex]
A similar problem is given at https://brainly.com/question/23508811
