## A Textbook Problem

For students of class 11-12 (age 16+)
HandaramTheGreat
Posts: 135
Joined: Thu Dec 09, 2010 12:10 pm

### A Textbook Problem

A TextBook Probability Problem:: there're $40$ students in a class among whom $20$ students play football, $25$ students play cricket and $10$ play both. if one is selected who plays football, then determine probability of his playing cricket.

so first i solved it in that way:: among $20$ students who play football, there're $10$ who play cricket also... then the answer is $\frac{10}{20}$ = $\frac{1}{2}$

then i found another solution:: there're total $35$ students who play at least one games, so probability of his playing football is $\frac{20}{35}$ and probability of his playing cricket is $\frac{25}{35}$ , then the answer is $\frac{20}{35}\cdot\frac{25}{35}$ = $\frac{20}{49}$

which one is wrong and why?

Shuvo
Posts: 3
Joined: Fri Dec 10, 2010 10:53 am

### Re: A Textbook Problem

The first one is right.
The second one is not right because you can't cut the five students out from the list and you must count them while calculating the probability.
There is a strong evidence for the first answer,I don't know,you know about the probability under a condition or not.For your kind information,I'm showing you that,
$P\frac {(Cricket)}{(Football)} = \frac {P(Cricket \bigcap Football)}{P(Football)}$
$= \frac {\frac {10}{40}}{\frac {20}{40}}$
$= \frac {1}{2}$

here is the probability of playing cricket with respect to playing football.
Do you have any confusion?????

kamrul2010
Posts: 120
Joined: Wed Dec 08, 2010 2:35 am
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### Re: A Textbook Problem

Why do you considering the probability of playing football?
You are already given with his football playing.
If computers have no doors or fences, who needs Windows and Gates?

Shuvo
Posts: 3
Joined: Fri Dec 10, 2010 10:53 am

### Re: A Textbook Problem

kamrul2010 wrote:Why do you considering the probability of playing football?
You are already given with his football playing.
I've considered the probability of playing football because there have been told to consider it.
if one is selected who plays football, then determine probability of his playing cricket.
This is the probability under certain condition.Here playing football is the condition and that's why you must have to consider it.

kamrul2010
Posts: 120
Joined: Wed Dec 08, 2010 2:35 am