Answer:
The probability that a student who completed the homework failed the test is 0.211.
Step-by-step explanation:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
The conditional probability of an event A given that another event B has already occurred is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Denote the events as follows:
P = a student passes the test
F = a student fails the test
X = a student completes the assignment
Y = a student does not completes the assignment
From the information provided the summary table is as follows:
P F Total
X 15 4 19
Y 2 6 8
Total 17 10 27
Compute the probability that a student completed the assignment and failed the test as follows:
[tex]P(X\cap F)=\frac{n (X\cap F)}{N}=\frac{4}{27}[/tex]
Compute the probability that a student completed the assignment as follows:
[tex]P(X)=\farc{19}{27}[/tex]
Compute the probability that a student failing the test given that the student completed the assignment as follows:
[tex]P(F|X)=\frac{P(X\cap F)}{P(X)}=\frac{4/27}{19/27}=\frac{4}{19}=0.21053\approx 0.211[/tex]
Thus, the probability that a student who completed the homework failed the test is 0.211.
