Respuesta :
Answer:
The probability that the selected student will be a student athlete is 0.32.
Step-by-step explanation:
Given : One student from a high school will be selected at random. Let A be the event that the selected student is a student athlete, and let B be the event that the selected student drives to school.
If P(A∩B)=0.08 and P(B|A)=0.25
To find : What is the probability that the selected student will be a student athlete?
Solution :
One student from a high school will be selected at random and the selected student will be a student athlete i.e. [tex]P(A)[/tex]
Using conditional probability,
[tex]P(B|A) =\frac{P(A\cap B)}{P(A)}[/tex]
[tex]0.25= \frac{0.08}{P(A)}[/tex]
[tex]P(A)= \frac{0.08}{0.25}[/tex]
[tex]P(A)=0.32[/tex]
Therefore, the probability that the selected student will be a student athlete is 0.32.
Using conditional probability, it is found that there is a 0.32 = 32% probability that the selected student will be a student athlete.
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The conditional probability 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 question:
- The probability of an student athlete being selected is P(A).
- We have [tex]P(A \cap B) = 0.08, P(B|A) = 0.25[/tex]
Thus, applying the formula:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]0.25 = \frac{0.08}{P(A)}[/tex]
[tex]0.25P(A) = 0.08[/tex]
[tex]P(A) = \frac{0.08}{0.25}[/tex]
[tex]P(A) = 0.32[/tex]
0.32 = 32% probability that the selected student will be a student athlete.
A similar problem is given at https://brainly.com/question/24161830
