Respuesta :
Answer:
The probability that a student passed the test given that they did not complete the assignment is [tex]\frac{15}{22}[/tex].
Step-by-step explanation:
The probability of an event E is the ratio of the number of favorable outcomes n (E) to the total number of outcomes N.
[tex]P(E)=\frac{n(E)}{N}[/tex]
The union of two events is:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
The intersection of the complements of two events is:
[tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]
The condition probability of an event given that another event has already occurred is:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
Denote the events as follows:
A = students who passed the test
B = students who completed the assignment
Given:
N = 27
n (A) = 17
n (B) = 22
[tex]n(A^{c}\cap B^{c})[/tex] = 3
Compute the value of P (A ∪ B) as follows:
[tex]P(A^{c}\cap B^{c})=1-P(A\cup B)[/tex]
[tex]P(A\cup B)=1-P(A^{c}\cap B^{c})[/tex]
[tex]=1-\frac{3}{27}\\[/tex]
[tex]=\frac{24}{27}[/tex]
Compute the value of P (A ∩ B) as follows:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]
[tex]=\frac{17}{27}+\frac{22}{27}-\frac{24}{27}\\[/tex]
[tex]=\frac{17+22-24}{27}[/tex]
[tex]=\frac{15}{27}[/tex]
Compute the value of P (A | B) as follows:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]=\frac{15/27}{22/27}[/tex]
[tex]=\frac{15}{22}[/tex]
Thus, the probability that a student passed the test given that they did not complete the assignment is [tex]\frac{15}{22}[/tex].
