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# help

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There’s 27 students, 18 play basketball and 16 play baseball. 3 students play neither sport. What’s the probability that a student chosen randomly from the class plays basketball or baseball?

Jan 30, 2020

#1
+78
+1

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Hi there...

If as you say, there's a total of 27 students.

And that 18 of them plays Basketball, 16 of them plays Baseball.
Collectively that equals a 1 in 27 choice, but only a 24/27 chance that one of them plays either sport.
But per sport, there's a 18 in 27 chance that the one picked would play Basketball.

Whilst there is a marginally smaller chance that the one picked would play Baseball, with 16 in 27 chance of that being the case.

As a side note...

There's a 3 in 27 chance that the one being picked would play neither sport.

I hope that helped a bit?

Kind regards

BizzyX

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Jan 30, 2020
#2
+18779
+2

Let's first find out how many play basketball (only), how many play baseball (only), and how many play both basketball and baseball.

There are 3 that do not play either sports, therefore, there are 27 - 3 = 24 students who play either baseball, basketball, or both.

Since there are 18 who play basketball and 16 who play baseball, there are 18 + 16 = 34 who play these sports.

But since there are only 24 players, some of these must play both.

34 - 24  =  10 -- which is the number who play both sports.

Removing these 10 students from the 18 who play basketball, there are 8 students who play only basketball.

Also, removing these 10 students from the 16 who play baseball, there are 6 student who play only baseball.

Summarizing:

There are 3 students who play no sports.

There are 8 students who play only basketball.

There are 6 students who play only baseball.

There are 10 students who play both basketball and baseball.

The probability that a student plays no sports is 3/27.

The probability that a student plays basketball (only) is 8/27.

The probability that a student plays baseball (only) is 6/27.

The probability that a student plays both sports is 10/27.

The probability that a student plays basketball is 18/27.

The probability that a student plays baseball is 16/27,

Jan 31, 2020
#3
+78
0

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Hi there...

The question was "What’s the probability that a student chosen randomly from the class plays basketball or baseball?".

The use of "OR" in a sentence implies "EITHER" not "BOTH".
And as such saying "24 in 27" is good enough of an answer in this context.
If you first decide to nitpick, you should add "14 in 27" to the list as well.

Kind regards

BizzyX

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BizzyX  Jan 31, 2020
#6
+108624
+1

To me it implies either or both.  It only excludes the 3 that do not play either.  That is why I believe the answer to be simply 24/27

Melody  Jan 31, 2020
#5
+108624
+2

There’s 27 students, 18 play basketball and 16 play baseball. 3 students play neither sport. What’s the probability that a student chosen randomly from the class plays basketball or baseball?

Actually the diagram was not needed.  It is just    24/27 = 8/9

Jan 31, 2020