Each of 5 ping pong balls is labelled with a different number from 1

Question

Each of 5 ping pong balls is labelled with a different number from 1 to 5. If three of the balls are selected at random, what is the probability that the median of the numbers on the selected balls is 3?

A) 1
B) 3/5
C) 2/5
D) 24/125
E) 1/5

A) 1
B) 3/5
C) 2/5
D) 24/125
E) 1/5

kpshabare · Answer

We have total of 5C3 possibilities, of which the median being 3 happens for 4 of the selections. So the answer is 4/5c3=4/10 . Option C.

Sent from my SM-A700FD using  GMAT Club Forum mobile app

Bunuel · Answer

Just to elaborate a bit. For the median to be 3, the selection should be one of the following:
{1, 3, 4}
{1, 3, 5}
{2, 3, 4}
{2, 3, 5}

So, we 4 favourable outcomes.

The total number of outcomes is  C^3_5=10 .

Thus the probability is 4/10 = 2/5.

Answer: C.

tanmeet · Answer

Numbers given- 1,2,3,4,5 
Step 1- Choose 3  (as this number has to be in the list as we need median as 3. )
Step 2- Select any no out of 2 nos which are less than 3( Only Options are 1 and 2).So 2c1
Step 3- Select any no out of 2 nos which are greater than 3( Only Options are 4 and 5).So 2c1
Total probabiliity of selecting 3nos out of 5 nos- 5c3  i.e 10
 So 2c1*2c1/5c3 
 Answer OPTION C. i.e 2.5

ScottTargetTestPrep · Answer

Let’s start by listing the outcomes in which we can select 3 balls and obtain a median of 3.

1, 3, 5

2, 3, 5

1, 3, 4

2, 3, 4

Thus, there are 4 ways in which we can select the balls such that we obtain a median of 3.
Since there are 5 balls and we are selecting 3 of them, the balls can be selected in 5C3 = 5!/3!2! = (5 x 4 x 3)/(3 x 2 x 1) = 10 ways.

Thus, the probability of drawing 3 balls such that the median is 3 = 4/10 = 2/5.

Answer: C

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Each of 5 ping pong balls is labelled with a different number from 1

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Each of 5 ping pong balls is labelled with a different number from 1

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards