Respuesta :
Answer: 0.857
Step-by-step explanation:
Let H represents the event of doing homework regularly,
And, E represents the event of doing well in the course,
Then, According to the question,
60% of the students do homework regularly.
⇒ The probability of doing homework regularly, P(H) = 60% = 0.60
⇒The probability of not doing the homework regularly, P(H') = 1 - P(H) = 1 - 0.6 = 0.4
Also, 80% of students who had been doing homework regularly, end up doing well in the course.
⇒ [tex]P(H\cap E) = 80\% \text{ of } 0.60= 0.48[/tex]
20% of students who had not been doing homework regularly end up doing well in the course.
⇒ [tex]P(H'\cap E) = 20\%\text{ of } 0.4 = 0.08[/tex]
⇒ [tex]P(E)=P(H\cap E) +P(H'\cap E) =0.48+0.08=0.56[/tex]
Thus, By the definition of conditional probability,
The probability that the student had been doing homework regularly,given that a student did well in the course,
[tex]P(\frac{H}{E})=\frac{P(H\cap E)}{P(E)}[/tex]
[tex]=\frac{0.48}{0.56}[/tex]
[tex]=0.857142857\approx 0.857[/tex]
