At an elite baseball camp, 60% of players can bat both right-handed

Question

At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

A.15%
B. 20%
C. 25%
D. 30%
E. 40%

A.15%
B. 20%
C. 25%
D. 30%
E. 40%

This appeared in a free test by Veritas Prep. I do not really understand the solution provided. Can someone explain please?

manpreetsingh86 · Accepted Answer

Let the total number of people who batted left handed = x
total number of people who bat left-handed, but do not bat right handed = x/4
thus x= 60 + (x/4)
or x=80

thus total number of people who batted right handed = 100-80 =20

thus required probability = (20/100)*100 = 20%

EMPOWERgmatRichC · Answer

Hi All,

This question can be considered an Overlapping Sets question (and solved with the Tic-Tac-Toe Board), but you don't need to organize your information in that way to get to the correct answer.

The key to this question is in realizing that some Left-handed batters ALSO bat with their Right-hands. Here's how you can answer the question by TESTing VALUES:

To start, let's choose 100 for the TOTAL number of players:

60% can bat with BOTH hands = 60 players

**Note: the TOTAL number of players who can bat with their LEFT hands include these 60 players AND the players who can bat with the Left hands ONLY.**

Next, we're told that 25% of players who can bat with their LEFT hands DO NOT bat with their Right hands.

X = Total who can bat Left-handed
25% of X DO NOT use their Right hands
75% of X CAN ALSO use their Right hands

Early on, we had 60 players who could bat with BOTH hands; THAT group is the 75% mentioned above...

.75X = 60
X = 80

There are 80 players who are Left-handed (20 are JUST Left-handed; 60 can bat with BOTH hands).

We're asked for the probability of randomly selecting a NON-Left-handed player.

Total = 100
NON-Left-handed = 20

20/100 = 20%

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

BrentGMATPrepNow · Answer

We can solve using the  Double Matrix Method .

The Double Matrix Method can be used for most questions featuring a population in which each member has two characteristics associated with it. 
Here, we have a population of baseball players, and the two characteristics are: 
- bats left-handed or DOESN'T bat left-handed
- bats right-handed or DOESN'T bat right-handed

NOTICE that the question does  not  ask us to find an actual number. It asks us to find a  probability . This means we can assign whatever value we wish to the total number of couples. 
So, let's say there are  100  players, which we'll add to our diagram:
 https://i.imgur.com/La2jgme.png

60% of players can bat both right-handed and left-handed  
60% of 100 = 60, so 60 players can bat both right-handed AND left-handed . 
Add that to the diagram to get:
 https://i.imgur.com/VMy3TRp.png

25% of the players who bat left-handed do not bat right-handed  
Hmmm, we don't know the number of left-handed players, so we can't find 25% of that value.
So, let's assign a variable. 
Let's let x = left-handed batters, and add it to our diagram: 
 https://i.imgur.com/837PZFm.png 
So, x of the 100 players bat left handed.

25% of the players who bat left-handed do not bat right-handed  
If x players bat left-handed, then 25% of x do not bat right-handed. 
In other words, 0.25x = number of players who do not bat right-handed
Add this to our diagram: 
 https://i.imgur.com/ol57Z2Y.png

At this point, we see that the two left-hand boxes add to x. 
So, we can write the equation: 60 + 0.25x = x
Rearrange to get 60 = 0.75x
Rewrite 0.75 as fraction to get: 60 = (3/4)x
Multiply both sides by 4/3 to get: 80 = x
If x = 80, then we know that 80 of the 100 players bat left-handed.
This means that the remaining  20  players DO NOT bat left handed.
 https://i.imgur.com/TJG8n0z.png

So, P(player doesn't bat left-handed) =  20 /100 = 20%

Answer: B

Cheers, 
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=jK-tiBrrf04

aeropower · Answer

Apparently, I don't understand it either.

Three options:

Both = .6
Right only = ?
Left only = .25

We are looking for Right only

1 - Both - Left only = .15

Right only = .15

Seem like the logical choice to me....

shriramvelamuri · Answer

Me too failed to undstnd this ques.

am i missing something.

jayanth7290 · Answer

I felt the explanation in the file attached might make the task easy ..Correct me If Im wrong

bethebest · Answer

I guess the tricky part is "25% of the players who bat left-handed do not bat right-handed". This also means that 75% of the players who bat left handed also bat right handed. 
=> 75%of left handed players = 60.
Therefore no. of left handed players = 80
Therefore number of players who bat only right handed = 20
Hence probability = 20/100 = 20%

Answer B

Please suggest if this approach is correct.

chetan2u · Answer

Hi,
your approach is correct..
Mention that you are starting with the total number as 100

gracie · Answer

let L=total left handed batters
L/4=left handed batters who do not bat right handed
L-L/4=3L/4=left handed batters who also bat right handed
let P=total players
3L/4=.6P
P=5L/4
L/(5L/4)=4/5=80% probability that player selected at random will bat left handed
100%-80%=20% probability that player selected at random will not bat left handed

SamBoyle · Answer

The trick is that it's a set problem and not a venn diagram.

So if 25% of the batters who bat left don't bat right that means it's 20%. As if 20 people don't bat right and 60% do then that's 2/8 or 25%

ScottTargetTestPrep · Answer

Solution:

We can let the total number of players = 100. So we have 60 players who can bat both right-handed and left-handed. We can let x = the number of players who can only bat left-handed. Thus, 40 - x = the number of players who can only bat right handed. We are given that 25% of the players who bat left-handed do not bat right-handed, which means they can only bat left-handed. Therefore, we can create the equation:

0.25(x + 60) = x

x + 60 = 4x

60 = 3x

20 = x

So we have 20 players who can only bat left-handed and also 40 - 20 = 20 players who can only bat right handed. We are asked for the probability that a player selected at random does not bat left-handed, i.e., who can only bat right-handed. Therefore, that probability is 20/100 = 20%.

Answer: B

fireagablast · Answer

60% R/L
25% of all L is NR/L

60+1/4x=x
60=3/4x
x=80

100-80=20

Hoozan · Answer

Could you explain how we can use NOT left and NOT right? Isn't NOT left = Right and NOT right = Left?

BrentGMATPrepNow · Answer

I used those terms in order to distinguish the four different categories of players:
1) bats left handed but not right handed
2) bats right handed but not left handed
3) bats left handed and right handed
4) bats neither left handed nor right handed

Fdambro294 · Answer

Assume 100 people

60% of the 100 people = 60 ppl are (L & R)

Assume L = total number of people who had Left Handed ——-> L will include:

Players who are (L ONLY)
+
Players who bat (L & R)

L = (L Only) + (L & R)

L = (L Only) + (60)

“25% of the batters who bat LEFT HANDED do not bat right handed”

Translated: 25% of the L total are part of (L Only)

This means that (100 - 25)% of the L total must bat BOTH (L & R)

75% * L = Both (L & R) = 60

(3/4)L = 60

L = 80

Out of the 100 people, 80 people bat Left Handed

The amount of people who do NOT bat Left Handed or (R Only) must be the remaining 20 people

Probability = 20 / 100

20 %

Posted from my mobile device

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At an elite baseball camp, 60% of players can bat both right-handed

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At an elite baseball camp, 60% of players can bat both right-handed

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