Contidional Probability?

please check the question, it is missing data - prababilities!
regards

fixed

not fixed yet

winner is ???????, what is the

[quote="sumithshah"]If the probability of Ben being the winner is ,


Please correct the question. Data missing.

sumithshah wrote:If Ben were to lose the championship, Mike would be the winner with a probability of 1/4 , and Rob 1/3 . If the probability of Ben being the winner is , what is the probability that either Mike or Rob will win the championship?

1/12 ; 1/7 ; 1/2 ; 7/12 ; 6/7

OA C


I have no clue how do this. Any pointers would be appreciated

This is the right Question

"If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob - 1/3. If the probability of Ben being the winner is 1/7, what is the probability that either Mike or Rob will win the championship?" Sumit would appreciate if u double check before posting a Question .. it would unnecessarily delay the posters time ....


here goes the Answer...

Prob of Ben wins=1/7

Prob of ben loses =6/7.

P(Mike wins or Rob wins) = P(Mike wins)+P(Rob wins) - P(Both wins)
=1/4+1/3-0
=7/12.

But we are only 6/7 sure about Ben loosing.

hence the probability is = 6/7*7/12=1/2

hope that helps....

P(Mike winning)=P(Ben looses). P(Mike wins) . P(Rob looses)
P(Rob winning)=P(Ben looses). P(Mike looses) . P(Rob wins)

Adding the two will give us the answer right?

Now given,P(mike wins)=1/4.Therefore,P(mike looses)=3/4
Similarly,P(rob wins)=1/3.Therefore,P(rob looses)=2/3
And,P(ben wins)=1/7.Therefore,P(ben looses)=6/7

Putting the values,
6/7.1/4.2/3 + 6/7.3/4.1/3 = 1/7+3/14=5/14

please explain where I am going wrong.

uptowngirl92 wrote:P(Mike winning)=P(Ben looses). P(Mike wins) . P(Rob looses)
P(Rob winning)=P(Ben looses). P(Mike looses) . P(Rob wins)

Adding the two will give us the answer right?

Now given,P(mike wins)=1/4.Therefore,P(mike looses)=3/4
Similarly,P(rob wins)=1/3.Therefore,P(rob looses)=2/3
And,P(ben wins)=1/7.Therefore,P(ben looses)=6/7

Putting the values,
6/7.1/4.2/3 + 6/7.3/4.1/3 = 1/7+3/14=5/14

please explain where I am going wrong.

You're double counting losses.

The only conditional part is Ben losing. There's no reason to multiply your individual events by the probability of Rob/Mike losing as well.

So, if you just want to add the two events:

Ben losing then Rob winning = 6/7 * 1/3 = 6/21 = 2/7

Ben losing then Mike winning = 6/7 * 1/4 = 6/28 = 3/14

2/7 + 3/14 = 4/14 + 3/14 = 7/14 = 1/2