Question

Please HELP on geometry I need this answer quick. At a high school, the probability that a student is a senior is 0.20. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.05. What is the probability that a randomly selected student plays a sport, given that the student is a senior. A: 0.15 B: 0.05 C: 0.25 D: 0.33

Answer 1

probability that a randomly selected student plays a sport, given that the student is a senior is 0.25

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

Answer 2

C: 0.25

Explanation:

We will use conditional probability formula to solve our given problem.

`P(B|A)=\frac{P(\text{A and B})}{P(A)}`, where,

`P(B|A)`= Probability of event B, given probability of event A.

`P(\text{A and B})`= Probability of event A and event B.

`P(A)`= Probability of event A.

Let us substitute our given values in conditional probability formula.

`P(B|A)`= Probability that a student plays a sport given that student is a senior.

`P(\text{A and B})`=The probability that a student is a senior and plays a sport = 0.05.

`P(A)`= Probability that a student is a senior = 0.20.

`P(B|A)=(0.05)/(0.20)`

`P(B|A)=(1)/(4)`

`P(B|A)=0.25`

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.