In Springville, the probability that a football team goes to the city playoffs is
0.20. The probability that the team goes to the state playoffs, given that the
team goes to the city playoffs, is 0.35.
What is the probability that a randomly selected team from Springville goes to
the city and state playoffs?
O A. 0.15
B. 0.55
O C 0.07
D. 0.70

Question

24-03-2022
Mathematics

contestada

In Springville, the probability that a football team goes to the city playoffs is
0.20. The probability that the team goes to the state playoffs, given that the
team goes to the city playoffs, is 0.35.
What is the probability that a randomly selected team from Springville goes to
the city and state playoffs?
O A. 0.15
B. 0.55
O C 0.07
D. 0.70

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joaobezerra joaobezerra · Answer 1 · 2022-04-07T09:43:48+02:00

Using conditional probability, it is found that the probability that a randomly selected team from Springville goes to the city and state playoffs is given by:

C 0.07

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: City playoffs.

Event B: State playoffs.

The given probabilities are P(A) = 0.2, P(B|A) = 0.35, hence the probability that a randomly selected team from Springville goes to the city and state playoffs is given by:

[tex]P(A \cap B) = P(A)P(B|A) = 0.2(0.35) = 0.07[/tex]

Hence option C is correct.

More can be learned about conditional probability at https://brainly.com/question/14398287