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).
