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

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:


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:


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:

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:


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.


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

Answer: B

Cheers,
Brent

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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....

Me too failed to undstnd this ques.

am i missing something.

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

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.

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

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

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%

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

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

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

100-80=20

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

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

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 %

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