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The probability that roger wins a tennis tournament (event a) is 0.45, and the probability that Stephan wins the tournament (event B) is 0.40. The probability of Roger winning the tournament, given that Stephan wins, is 0. The probability of Stephan winning the tournament given that Roger wins, is 0. Given this information, which statement s true?

Sagot :

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Answer:

3.Events A and B are not independent because P(A|B) ≠ P(A).

Step-by-step explanation:

Given this information, which statement is true?

1.Events A and B are independent because P(A|B) = P(A).

2.Events A and B are independent because P(A|B) ≠ P(A).

3.Events A and B are not independent because P(A|B) ≠ P(A).

4.Events A and B are not independent because P(A|B) = P(A).

Solution:

Two events A and B are independent if A occurring does not change the probability of B. For independent events:

P(A ∩ B) = P(A) * P(B)

Hence: P(A/B) = P(A ∩ B) / P(B) = P(A) * P(B) / P(B) = P(A)

Let event A represent the probability that roger wins a tennis tournament and event B represent the probability that Stephan wins a tennis tournament.

Therefore:

P(A) = 0.45, P(B) = 0.4

The probability of Roger winning the tournament, given that Stephan wins, is 0. Hence, P(A/B) = 0

P(A/B) = P(A∩B) / P(B)

0 = P(A∩B) / 0.4

P(A∩B) = 0

The probability of Stephan winning the tournament given that Roger wins, is 0. Hence P(B/A) = 0

P(B/A) = P(B∩A) / P(A)

0 = P(B∩A) / 0.4

P(B∩A) = 0

Therefore since P(A∩B) = P(B∩A) =0, this means that event A and event B are mutually exclusive. That is both events cannot occur at the same time.

Events A and B are not independent because P(A|B) ≠ P(A).

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