Considering the definition of conditional probability, the probability that the team will win the second game given that they have already won the first game is 45.33%.
<h3>Definition of probability</h3>
Probability is the greater or lesser chance that a given event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
<h3>Conditional probability</h3>
Conditional probability is the probability that a given event will occur given that another event occurs. The conditional probability operator is the │ sign.
In other words, the conditional probability is the probability of some event A , given the occurrence of some other event B and is denoted by P(A|B) and is read “the probability of A , given B ”.
Then, when an event influences the outcome of a second event, the probability of the second event is said to be a conditional probability and is calculated using the expression:
P(A|B)= P(A∩B) ÷ P(B)
where:
- the probability of event B cannot be zero.
- P(A∩B) is the probability of both events happening.
<h3>Probability that the team win the second game</h3>
In this case, you know that:
- B: The baseball team win the first game.
- A: The baseball team win the second game.
- The probability that they will win both games is 34% → P(A∩B)= 0.34
- The probability that they will win the first game is 75% → P(B)= 0.75
Replacing in the definition of conditional probability:
P(A|B)= 0.34 ÷ 0.75
<u><em>P(A|B)= 0.4533= 45.33%</em></u>
Finally, the probability that the team will win the second game given that they have already won the first game is 45.33%.
Learn more about conditional probability:
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