Question

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 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).

Answer 1

So assuming that this is the same turnament
the results are dependent of each other
I'm not sure about the P(A|B) not equal to P(A) part
but the answer is either 3 or 4

Answer 2

Answer:

Hence, option (3) is correct.

Step-by-step explanation:

The probability that Roger wins a tennis tournament (event A) is 0.45 i.e. P(A)=0.45

The probability that Stephan wins the tournament (event B) is 0.40 i.e. P(B)=0.40

The probability of Roger winning the tournament, given that Stephan wins, is 0 i.e. $P(A|B)=0$

The probability of Stephan winning the tournament, given that Roger wins, is 0 i.e. $P(B|A)=0$

We know that $P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

⇒   P(A∩B)=0

But if A and B are independent events then P(A∩B)=P(A)×P(B)

Hence, P(A|B)=P(A)

Similarly $P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}$

Hence, if A and B are independent events then,

P(B|A)=P(B)

But in this situation such a thing is not possible.

Hence, option (3) is correct.