In a genetic database of 200 samples, each sample may or may not show

Question

In a genetic database of 200 samples, each sample may or may not show Marker X, and each sample may or may not show Marker Y. Every sample that does not show Marker X also does not show Marker Y. Exactly 150 samples show at least one marker, and exactly 120 samples do not show Marker Y.

One sample is selected at random. Select for  P(X only)  the probability that the sample shows Marker X but not Marker Y, and select for  P(Both)  the probability that the sample show s both markers. Make only two selections, one in each column.

Bunuel · Accepted Answer

The possible states for a sample are:

• (X yes, Y yes)
• (X yes, Y no)
• (X no, Y no)

The state (X no, Y yes) is impossible, because the rule says if X is absent then Y must also be absent.

From the information given, the total is 200.

Since 120 samples do not show Y (the Y no groups), we know that the remaining 80 show Y. These must be (X yes, Y yes). So, (X yes, Y yes) = 80.

Also, 150 samples show at least one marker, which must be X, because Y cannot appear without X. Therefore, X = 150, which means (X yes, Y yes) + (X yes, Y no) = 150. This makes, (X no, Y no) = 200 - 150 = 50.

Now we can break down the counts:

• (X yes, Y yes) = 80
• (X yes, Y no) = total − (X yes, Y yes) − (X no, Y no) = 200 − 80 − 50 = 70.
• (X no, Y no) = 50

Finally, we calculate the required probabilities:

P(X only) = 70/200 = 0.35.

P(Both) = 80/200 = 0.40.

Answer:  P(X only) = 0.35, P(Both) = 0.40

I29-176

Mehta17 · Answer

to solve the problem, let's define:

Total samples = 200

Samples showing at least one marker = 150

Samples not showing marker Y = 120

Samples not showing marker X also do not show marker Y

From the above:

The 50 samples that do not show any marker are (200 - 150).

Since every sample that does not show Marker X also does not show Marker Y, these 50 samples are "no marker" samples, so samples that do not show X = samples that do not show Y plus samples that show Y but no X (to be found).

Given 120 samples do not show marker Y, so samples showing Y = 200 - 120 = 80.

Thus, samples showing X = total samples - samples not showing X = 200 - 50 = 150.

Now:

P(X only)
P(X only) = samples that show X but not Y.

P(Both)
P(Both) = samples that show both X and Y.

Let's find these counts:

Samples showing Y = 80
Samples showing both X and Y = 80 − 80− samples showing Y but not X (which is zero because if sample does not show X, it does not show Y). So all samples showing Y also show X.

Hence, samples showing both X and Y = 80.

Samples showing X only = Samples showing X - Samples showing both = 150 - 80 = 70.

Now probabilities:

P(X only)=70 /200=0.35
P (Both)=80/200=0.4

AbhishekP220108 · Answer

https://gmatclub.com/forum/download/file.php?id=86033 Here’s the Venn diagram: X only = 70 Y only = 0 (forbidden by the condition if no x, then no y) Both = 80 Neither = 50 Each sample can fall into one of 4 categories: Both X and Y → let’s call this bbb. X only → x. Y only → y Neither → n. So, total =b+x+y+n=200 But from the condition: "no Y-only samples" ⇒ y=0 So b+x+n=200 x+n=120 n=120−x b+x=150 b+x+(120−x)=200 b+120=200 b=80 substituting b in above equations we get x=150−80=70 n=120−70=50 so P(xonly)=70/200=0.35 P(both)=b/200=80/200=0.4 GMAT-Club-Forum-pt9cx41g.png

PTanjiro · Answer

200 samples in all.
Exactly 150 show at least one of X,Y thus,  50 show none .

120 don't have Y meaning 120 have X or have none.  Therefore Only X is 70 . (50 have none) 
80 will have Y or both X & Y.

The statement: If xX then xY is also considered as If Y then X.   Thus all Ys should be in X.  
You can draw a Venn diagram and thus you will get 80 in the intersecting portion. Only Y will be 0 and Only X will be 70.

A great question!

Dereno · Answer

The total number of samples = 200

Let’s take a 4x4 matrix.

given that :

1) Every sample that does not show Marker X also does not show Marker Y.

2) Exactly 150 samples show at least one marker.

3) exactly 120 samples do not show Marker Y.

X  
 Not X  
  Total  
 
   Y  
  80 
  0  
  y = 80 
 
  NOT Y

120  
 
   Total  
  x  
  
   200

y = 200 -120 = 80

as per note 1: Not X is 0.

given that alteast 1 marker = 150 = x + y , with y= 80, then x = 70.

P ( X only) = 70/200 =  0.35

P ( Both) = 80/200 =  0.40

In a genetic database of 200 samples, each sample may or may not show

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P(X only)	P(Both)
		0.2
		0.3
		0.35
		0.4
		0.6
		0.7

GMAT Two-part Analysis (TPA) Questions

In a genetic database of 200 samples, each sample may or may not show

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