Respuesta :
Answer:
0.75 = 75% probability that she knewthe answer to that question
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It 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 question:
Event A: Answered correctly.
Event B: Knew the answer.
Probability of answering correctly:
0.5(knows the answer)
1/3 of 1 - 0.5 = 0.5(didn't know but guessed correctly). So
[tex]P(A) = 0.5 + 0.5\frac{1}{3} = 0.6667[/tex]
Probability of answering correctly and knowing the answer:
0.5, which means that [tex]P(A \cap B) = 0.5[/tex].
What is the probability that she knew the answer to that question?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.5}{0.6667} = 0.75[/tex]
0.75 = 75% probability that she knewthe answer to that question
