Respuesta :
Answer:
C: 0.25
Step-by-step explanation:
We will use conditional probability formula to solve our given problem.
[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,
[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.
[tex]P(\text{A and B})[/tex]= Probability of event A and event B.
[tex]P(A)[/tex]= Probability of event A.
Let us substitute our given values in conditional probability formula.
[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.
[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.
[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.
[tex]P(B|A)=\frac{0.05}{0.20}[/tex]
[tex]P(B|A)=\frac{1}{4}[/tex]
[tex]P(B|A)=0.25[/tex]
Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.
Answer:
probability that a randomly selected student plays a sport, given that the student is a senior is 0.25
Step-by-step explanation:
Let, A be an event that a student is senior.
Probability can be given as , p(A) = 0.20
B be the event where student plays a sport
Probability can be given as , p(B) = 0.15
We have given that the probability of a student is a senior and plays a sport is 0.05.
i.e p(A∩B) = 0.05
We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .
Use the formula: p(B/A) = p(A∩B) / p(A)
Plug corresponding values to get p(B/A).
p(B/A) = p(A∩B) / p(A) = 0.05 /0.20
p(B/A) = 0.25 , this is the answer
