Respuesta :
Using conditional probability, it is found that there is a 0.12 = 12% probability that a student gets an A in Algebra 2 and does all their assignments.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
- P(B|A) is the probability of event B happening, given that A happened.
- [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem, the events are:
- Event A: Student gets an A in Algebra 2.
- Event B: Student completes all the assignments in Algebra 2.
The probabilities are:
- The probability that a student gets an A in Algebra 2 is 0.2, hence [tex]P(A) = 0.2[/tex].
- The probability that a student completes all the assignments in a Algebra 2 is 0.5, hence [tex]P(B) = 0.5[/tex].
- The probability that a student does all their assignments given that they get an A in Algebra 2 is 0.6, hence [tex]P(B|A) = 0.6[/tex].
We want to find [tex]P(A \cap B)[/tex], hence:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]0.6 = \frac{P(A \cap B)}{0.2}[/tex]
[tex]P(A \cap B) = 0.6(0.2) = 0.12[/tex]
0.12 = 12% probability that a student gets an A in Algebra 2 and does all their assignments.
You can learn more about conditional probability at https://brainly.com/question/14398287
