There are 5 semi-finalist, including John and Maria. If there is no

Question

There are 5 semi-finalist, including John and Maria. If there is no ties, what is the probability that Maria gets a better position than John?

A.  \frac{1}{6}

B.  \frac{1}{3}

C.  \frac{1}{2}

D.  \frac{2}{3}

E.  \frac{5}{6}

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ThatDudeKnows · Accepted Answer

We have no reason to be biased toward putting either of them earlier in the ranking than the other. Half the time, John will beat Maria; half the time, Maria will beat John.

Answer choice C.

Axwe7 · Answer

Is there a mathematical explanation for the answer?  Bunuel

Bunuel · Answer

Maria and John can finish in either order:

a. Maria ahead of John
b. John ahead of Maria

Since there are no ties, these two cases are equally likely.

So the probability that Maria gets a better position than John is 1/2.

Answer: C.

agrasan · Answer

Think like there are five spots for ranking in the order: 1, 2, 3, 4, 5.

Let's say we put Maria at 1 then we can put John at one of 2,3,4,5. Other 3 players can be arranged in 3! ways. Total ways = 4*3!
If we put Maria at 2 then we can put John at one of 3,4,5. Other 3 players can still be arranged in 3! ways. Total ways = 3*3!

Similarly, we will have 2 more cases.

Total number of arrangements = 5!

Probability = 3!*(4+3+2+1)/5! = 1/2

BongBideshini · Answer

Among all possible rankings of the 5 semifinalists, John and Maria can be ordered in only two ways:
 
 Maria finishes ahead of John. 
 John finishes ahead of Maria.  
Since there are no ties and neither person has any advantage over the other, these two outcomes are equally likely.
Therefore, the probability that Maria gets a better position than John is:
1/2

Answer: C

paragw · Answer

Ctrl+C and Ctrl+V seem to have skipped the "Read the Question" step.

ankushsambare · Answer

You've copy pasted so hard that even the question is confused.

paragw · Answer

And arrived at the wrong address.

There are 5 semi-finalist, including John and Maria. If there is no

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GMAT Problem Solving (PS) Questions

There are 5 semi-finalist, including John and Maria. If there is no

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