Answered

From health tips to tech hacks, find it all on IDNLearn.com. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.


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).

Sagot :

Apologiabiologyidn
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:

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. [tex]P(A|B)=0[/tex]

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

We know that [tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

⇒   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 [tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

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.

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.