4TH day: SOLVE THIS INTERESTING PROBLEM

I SAID,I WOULD POST A QUESTION DAILY FOR DISCUSSING AMONG YOURSELVES..... SO HERE IS A NEW PROBLEM FOR TODAY.....THANKS TO ALL WHO JOINS THIS DISCUSSIONS .....WISHING ALL THE BEST.......:-)

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

I AM HERE GIVING THE SOLUTION......TODAY I WOULD POST A NEW QUESTION....:).... If the integer is 1 its probability is log(1),if the integer is 2 its probability is log(2),if the integer is 3 its probability is log(3)……likewise if the integer is n then its probability is log(n)……..let A denote the statement that the chosen number is even…..and B denote the statement that the chosen number is 2…. So (A intersection B)=2……hence the required probability is P(B/A)=[P(A intersection B)]/P(A)=P(B)/P(A)=log(2)/[log(2)+log(4)+log(6)+log(8)+…….log(2n)] =log(2)/log[(2^n)n!]=log(2)/[nlog(2)+log(n!)]………….thanx for joining....:).....try my new problem.....

Sayan Chaudhuri - 8 years, 1 month ago

Should not the answer be $\frac {log(2)}{n}$ ?

Aditya Parson - 8 years, 1 month ago

Since number of positive even integers for first $2n$ numbers is simply $\frac{2n}{2}=n$ . And, probability of getting 2 from all even integers can be expressed as $\frac{log 2}{n}$ , according to the question

Aditya Parson - 8 years, 1 month ago

sorry,your understanding about the question is wrong....please go through the question minutely.....you have not understood it......try it...best of luck....:)

Sayan Chaudhuri - 8 years, 1 month ago

@Sayan Chaudhuri – Can you point out my mistake, given that you have already solved it.

Aditya Parson - 8 years, 1 month ago

@Aditya Parson – i have already solved it.....:)...here you must think of conditional probability......that's my last hint.....try to think of this statement.......when we pick a number it is 2 given that the number is even........now i have almost said you what to do.......best of luck.....:)

Sayan Chaudhuri - 8 years, 1 month ago

I am getting the answer as $\frac{log(2)}{n*log(2) + log(n!)}$

Saurabh Dubey - 8 years, 1 month ago

mine is the same.....then, you are right absolutely........could you prove your result.......??......:)

Sayan Chaudhuri - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$