#Probability

130 messages · Page 1 of 1 (latest)

carmine obsidian
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can someone help with this ques

harry larry and carry doing tosses one after another. harry goes first, larry goes second and carry goes third.
harry has a 4/5 chance of actually making a toss or else it gets passed to larry

find winning probability of carry if first one to get a head wins?

rare bluffBOT
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unreal valley
carmine obsidian
unreal valley
carmine obsidian
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Harry and Larry and Carry take turns tossing a coin with harry going first, larry going second. The first to toss a head wins. What is the probability that carry wins?

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Harry has got drunk and now he has a 4/5 chance of actually making a toss. If he dosen't the turn passes to Larry

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What is the probability that Carry wins now?

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this is what i was sent

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@unreal valley

unreal valley
carmine obsidian
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idk where he got this from

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are u still not able to get the question

unreal valley
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It's clearer.

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Pain in the ass to calculate, though, even before the curveball.

keen prairie
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Of cases where carry wins

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And there probabilities

carmine obsidian
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yes i made 5 cases

keen prairie
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it's an infinite series

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U need to use a/1-r

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I'm lazy to make it for u though it's a bit more complex

carmine obsidian
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  1. Harry tosses and wins
  2. Harry doesn't tosses and it gets passed to Larry and he wins
  3. It gets passed to larry but carry wins
  4. Harry does a toss but larry wins
  5. Harry does a toss but carry wins
keen prairie
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As I said , it's infinite

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U can keep making cases

carmine obsidian
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then I calculated them individually using the a/1-r formula

keen prairie
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Individually??

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U need to add them

carmine obsidian
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these 5 cases

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i mean

carmine obsidian
keen prairie
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P(a)+p(b)+p(c)...

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U have to make just one function and use the formula not multiple

carmine obsidian
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how

keen prairie
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Let's take an example

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A simpler one

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A and B take turns tosing a coin

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First to head wine

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Wins

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A GOES first

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Now tell me probability of A@carmine obsidian

carmine obsidian
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of A winning

H
TTH

1/2/1-1/4

= 2/3?

keen prairie
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No..

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H+tth+tttth+tttttth...tttttttttttth...

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Got it?

carmine obsidian
keen prairie
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U took literally just the first two

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Wait no

carmine obsidian
keen prairie
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Uhh

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The answer of this one was 6/11 lol

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Idk what's wrong here

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But this is the method yes

carmine obsidian
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6/11? 🤔

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might be a biased coin

keen prairie
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Nah

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Fair coin

carmine obsidian
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uh

keen prairie
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Ah okay it's 2/3

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Maybe that was sm other ques

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So yeah this ques is similar to that

carmine obsidian
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yeah

keen prairie
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Just find the ratio

carmine obsidian
keen prairie
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It's just that A' probability isnt 1/2 but 9/10

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A' means A complement

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Wait no

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6/10 yeah

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Caus he needs to throw a toss and get head to win

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Subtract that from 1

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And u get A complement

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Also multiply B's failing chances

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That's your common ratio

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@carmine obsidian

carmine obsidian
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🧐

carmine obsidian
keen prairie
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I corrected myself

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6/10

carmine obsidian
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i mean how 6/10

keen prairie
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What's the probability he gets a head

carmine obsidian
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1/2

keen prairie
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No

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4/10

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Caus he needs to toss to get a head

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4/5*1/2

carmine obsidian
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oh right

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4/10 yes

keen prairie
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Minus that from one

carmine obsidian
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6/10 of not getting a head

keen prairie
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Then I think u get it now

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Yes

carmine obsidian
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BUT

keen prairie
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And also u need to multiply A's failing chances

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And C

carmine obsidian
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won't it go like

H + TTTH + TTTTTTH
Again

keen prairie
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YES IT would

carmine obsidian
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and for each toss he would have a 4/5 chance

keen prairie
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But don't forget in A's case heads and not heads isn't equally likely

carmine obsidian
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4/5H + (4/5)² TTTH + (4/5)³ TTTTTTH + ...

keen prairie
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why are u cubing it

carmine obsidian
keen prairie
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4/5 stays

carmine obsidian
keen prairie
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Yeah so for each time it stays 4/5

carmine obsidian
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4/5H ~> one toss only + (4/5)² TTTH ~> two toss + (4/5)³ TTTTTTH ~> three tosses + ...

keen prairie
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bruh if u toss a head in first try are u gonna have a 1/4fh chance of tossing it in second try

carmine obsidian
keen prairie
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It's the same thing here

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The chances of him tossing don't change

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Just take 4/5 and solve u will get correct answer

carmine obsidian
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alrightttt

keen prairie
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Oh wait yeah ur right

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@carmine obsidian

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I forgot ur tossing more than once

carmine obsidian
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mhm

keen prairie
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xd

carmine obsidian
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xd

keen prairie
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U don't need to take it separately

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R=4/5*1/2*1/2

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Wait not

carmine obsidian
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4/5 x 1/8

keen prairie
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R=6/10*1/2*1/2

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Caus we multiplying fail chances

carmine obsidian
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okay

ruby jewelBOT
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@carmine obsidian

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drifting frigate
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+close