FUn questions - Probability - help!!!

[apoechma]

Hello! I need help understanding how to get to the answers on this question. I would be sooo appreciative if someone woule write it out and explain it, as once I understand this I can understand a lot more!! I REALIZE they are VERY BASIC!!! so for many it will be easy, for me its not so easy!!!

Here we go!!!!

IN an upcoming race, athletes have to finish first, second, or third in order to be selected for the team. The probabolity that John will finish in the top 3 is .40, wereas the probability that bill will finish in the top 3 is only .25. However, if John doesnt finish in the top 3, then Bills probabiltiy of finishing in the top 3 increases to .35. IF Bill was to finish in the top 3, what is the probability that Jogn will get on the olympic team?

The answer is .16.

Please how do we get there? I think we use the equation of P(A/B)= P(AnB)/ P(B)?

Thank u!!!

[Enuma_Elish]

P(J|B)P(B) = P(JnB) = P(BnJ) = P(B|J)P(J) .

[apoechma]

Im still having a hard time, cud someone please put the numbers into the equation for me? Once I see this I will understand SO MANY more questions!!! THank you sooo mUCH!!!!

[Enuma_Elish]

IN an upcoming race, athletes have to finish first, second, or third in order to be selected for the team. The probabolity that John will finish in the top 3 is .40, wereas the probability that bill will finish in the top 3 is only .25. However, if John doesnt finish in the top 3, then Bills probabiltiy of finishing in the top 3 increases to .35. IF Bill was to finish in the top 3, what is the probability that Jogn will get on the olympic team?

P{J} = 0.4; P{B} = 0.25; P{B|~J} = 0.35; P{J|B} = ?

Law of total probability, or Bayes's Law:
P{B} = P{B|J}P{J} + P{B|~J}P{~J}
0.25 = P{B|J} 0.4 + 0.35 (1-0.4)
Solve for P{B|J}, call it x

From the definition of conditional prob.:
P{JnB} = P(BnJ) = P(B|J)P(J) = x P{J} = x 0.4
P{J|B} = P{JnB}/P{B} = x 0.4/0.25

EnumaElish
___________________________________________
I would definitely have logged in as EnumaElish had PF administration awarded that account the privilege of posting replies, after I reset my e-mail address Tuesday, October 28, 2008.

[apoechma]

Thank u!