2 Probability problems (1 Viewer)

juantheron · Apr 8, 2016

$$(1)\; Two point $P$ and $Q$ are taken on straight line $OA$ of length $a$ unit$

$Then the probability that $PQ>b\;$ unit, Where $a>b$

$(2)\; The decimal part of logarithm of two numbers taken at random are$

$found to $7$ places , Then the probability that second number can be$

$subtracted from first number$

Paradoxica · Apr 8, 2016

juantheron said:
$$(1)\; Two point $P$ and $Q$ are taken on straight line $OA$ of length $a$ unit$

$Then the probability that $PQ>b\;$ unit, Where $a>b$

$(2)\; The decimal part of logarithm of two numbers taken at random are$

$found to $7$ places , Then the probability that second number can be$

$subtracted from first number$

I don't understand either of those problems. Please attempt to word them better.

InteGrand · Apr 8, 2016

Paradoxica said:
I don't understand either of those problems. Please attempt to word them better.

I assume for the first one:

$\noindent There's a line of length $a$ units (where $a$ is a fixed positive real number). The points $P$ and $Q$ are chosen randomly (uniformly) on this line. Let $b$ be a fixed real number satisfying $0\leq b \leq a$ (I know he put $b < a$, but we can include $b=a$ and it doesn't change anything much, and it's good to keep as an extreme case). Find the probability that the length of $PQ$ will exceed $b$.$

InteGrand · Apr 8, 2016

Haven't thought too much about the second part but my guess for it is:

$\noindent Two numbers $X_1$ and $X_2$ (greater than 0) are randomly chosen. Then the fractional parts of $\ln X_1$ and $\ln X_2$ are computed and rounded to seven decimal places (call these $F_1$ and $F_2$ respectively). What is the probability that $F_1 \geq F_2$?$

$\noindent I think for this one we'd need a distribution to be specified for $X_1$ and $X_2$, since they have an infinite support and we can't assume a uniform distribution for that. And I think that if $X_1$ and $X_2$ are specified the same distribution, then the answer to the probability would just be $\frac{1}{2}$ by symmetry (or it would be if the question didn't include rounding; with rounding, I think it'll be less than half, since the probability that $F_1$ and $F_2$ are equal will be non-zero).$

juantheron · Apr 8, 2016

Yes InteGrand I mean same thing, You explained very well

InteGrand · Apr 8, 2016

juantheron said:
Yes InteGrand I mean same thing, You explained very well

For the second one, do you know whether any distributions were specified?

Paradoxica · Apr 8, 2016

How does this thread have 0 views wtf... Do we not count as people?

InteGrand · Apr 8, 2016

Paradoxica said:
How does this thread have 0 views wtf... Do we not count as people?

It takes a bit of time for the view count to update I think.

2 Probability problems (1 Viewer)

juantheron

Active Member

Paradoxica

-insert title here-

InteGrand

Well-Known Member

InteGrand

Well-Known Member

juantheron

Active Member

InteGrand

Well-Known Member

Paradoxica

-insert title here-

InteGrand

Well-Known Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)