Help Me Out Guys

Sorry for the delay, guys. Something came up, and I was a little tied up for a while. Unfortunately, I’ll only be able to serve you the “sponsored dish” after this post — won’t take long. Meanwhile, I need your help on some mathematics. I was never good at questions like these, so any help from you guys will be greatly appreciated.

Please help me out, yea? I seriously need to know how to answer the question below. It’s some sort of a possibility (kebarangkalian — in Malay) question. If possible, can you include the formula and the answer as well? That’s because I have 2 similar questions. So if you provide the formula, I should be able to answer the next question myself (I hope).

The question goes something like this:

1. There are 3 people in 3 separate classrooms.
2. There are 10 different color pencils on the table (red, blue, green, …) of each classroom.
3. There are 50 numbers to choose (ie. 1, 2, 3, 4, 5, 6, … 48, 49, 50).
4. The 3 people need to write down 2 different numbers (between 1 to 50) on a paper.
5. What is the possibility of all 3 people using the same color pencil and writing the same numbers.

I feel like a fool for not knowing how to do such simple mathematics. I hope you guys can really help me out with this one. *Quite urgent* Thanks in advance!

**********

UPDATE:
My initial explanation might not be perfect. So I’m adding more detailed information.

Each person can only choose 1 type of color pencil. Both numbers must be written with the same color. Both numbers must be different.

Example:
All 3 people used blue color pencil to write the numbers 12 and 24.


26 thoughts on “Help Me Out Guys

  1. Freethinker says:

    Shiat… though I learn some advance stuff.. when come to these, I forgot already… this 1 I tembak one ….

    meaning 1 – Probability ( item 5 )
    Probability item 5 is (50C48) X ( 10C9 ) and then to power of 3….for 3 ppl..

    and use 1 – that above to get the common goal…

    C is permutation… err u c advance calculator got that button 1 la..

    OOI… this 1 i tembak 1 arr… but idea roughly like this la…

    NOW SHOW ME THE NEW POST !!!

    if wrong dun shoot me la…

  2. Freethinker says:

    Err.. Jee,choosing 2 numbers from 50, urs is a bit doubtful plus.. unlikely yo multiple with 1/3… probability theory rarely multiple wif fraction.. using powers are usually the case to articulate a duplication effect of multiple repetitive..

    again i maybe wrong..

    HAHA..simply tembak la

  3. TenthOfMarch says:

    @Jee
    Thanks, Jee. I did think of something like that as well, but wasn’t too sure about it. We’ll see what the others have to say. Thanks again.

    @Freethinker
    Wahhh…your formula looks complex. But mathematics are complex. hahaha. I was thinking “what the heck is the ‘C’?” Then I remembered what it was. Hehhee.

    Thanks for your info, yeah. I’ll use it immediately after at least one other person confirm it. It’s quite important, can’t have any mistake.

    @Boss Lepton
    Well…each person can only choose 1 color out of the 10 colors. They need to use the same color to write both the numbers. BTW, both the numbers must be different.

  4. Boss Lepton says:

    Ok la, suppose a same person cannot reuse the same colour pencils twice.

    Then let’s think it this way

    we know that choosing colour pencils and writing numbers are 2 independent events.

    This implies probability of choosing same colour pencils and writing same numbers is equal to

    P(choose same colour pencils) * P(writing same numbers)

    There are 10C2 ways of choosing 2 colour pencils for each person, so the probability of of choosing same colour pencils is (1/45)^3

    There are 50C2 ways of choosing 2 numbers from 50, so P(writing same numbers) is (1/(25*49))^3

    multiply the numbers together and i think that’s the answer, quite low chance I would say…….

    dunno if i’m correct or not la

  5. TenthOfMarch says:

    If I were to follow Freethinker’s formula, it would work out as:
    (1225 X 10)^3 = 12250^3 = 1.838265625 X 10^12

    Errrr…correct or not? Hehehehee. Means how do you “call it”? The possibility of that happening is “1 in 1.838265625 X 10^12 times”?

  6. Boss Lepton says:

    Ok here’s a better explanation

    two person choosing same colour has probability 1/10 (since it only take the 2nd person to choose the same colour as the 1st person, we can fix the first person)

    Similarly, three person choosing same colour has probability 1/100

    There are 50C2 ways of choosing the numbers

    Therefore two person choosing same numbers will be 1/(50C2)

    Similarly, 3 person choosing same numbers will be 1/(50C2)^2

    Multiply the numbers to get the probability you want which I got 6.7 * 10^(-9)

    should be correct this 1 :D

  7. Freethinker says:

    EH, Lepton, all my buku dunno fly where..u sure got stats ref.. find for him la..

    I WANNA C NEW POST !!!!

    HAHHA

    Jee almost confirm sure wrong..definately using factorial/ permutatation concept…

    U can use mine and lepton’s theory to finalise…

    I simply tembak 1 arr..yesterday nite watch HEROES and 24 , almost half blur 1…

  8. Freethinker says:

    Oups there’s a flaw in mine, my C stuff get combinations , not probability… but gist almost then same…

    OK..if numbers and colour are fixed.. that means there’s wont be a probability regarding combination of colour and numbers…

    So Tembak round 2… :

    2 to choose from 50 is 2/50
    1 to choose from 10 is 1/10

    2/50 X 1/10 is probability getting a SPECIFIC colour and number….for 1 person..

    Power 3 for 3 person…

    NIAMA, y simple maths I cant do already 1….basket betul

  9. Freethinker says:

    basket.. in office so long, do ur math onli..u need to clarify ONE thing clear. IS SAME COLOUR or JUST BLUE.

    SAME COLOUR = Lepton correct
    JUST BLUE = ( (1/50C2)(1/10) ) power 3.. probability is MUCH smaller than Lepton because it is narrowing down to one SPECIFIC NUMBER NOT POSSIBILITY OF EITHER RED/BLUE/YELLOW……

    Hope it helps, for the last time…any math geeks out there, help the fella la !!!

  10. TenthOfMarch says:

    @Freethinker
    At the end, the 3 people can choose *ANY* one of the 10 colors. So, it means as long as at the end, all 3 people are using the *SAME* colors — doesn’t matter what color it is.

    Hahahha, whole morning do my question only? Not scared boss angry. LOL! Don’t worry…I assure you guys that helping me with this question, will be “rewarding”. You will know why *soon enough* ;-) .

    @Boss Lepton
    Wow, thanks. Your explanation is very clear. So, based on your calculations, correct me if I’m wrong:

    If the possibility is 0.1, that means, it is 1 in 10 cases (1 / 0.1 = 10).

    If the possibility is 6.7 * 10^(-9), that means, it is 1 in 149,253,731 cases (1 / 6.7 * 10^(-9) = 149,253,731)?

  11. aw says:

    I think the more common term is “probability”. But yeah if 6.7 * 10 ^ (-9) is correct, then that scenario will only happen once in about 149K times if the “experiment” is carried out an infinite number of times.

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  13. aw says:

    *snarky comment ahead*

    Don’t worry about whether accurate or not. The A*****lets way will be:

    Step 1:
    Declare “With our years of experience (we registered poofy.com in 1992), we calculated that the probability is 1 in 15,235. The other guy cannot calculate this correctly one. If we do get it wrong, feel free to do our job for us and correct us.”

    Step 2:
    “What do you proport to mean that you are insinuating that it is in actuality 1 in 149M? Are you anti-A*****lets?? Liaise with me at my mobile number and I will show you our tested construct. Your claim is entireless baseless and you are antagonistic. We will have wine. And make sure your England is powderful, because mine is.”

    Step 3:
    “Oh the calculation was in beta. But we will leave the declaration up anyway.”

  14. TenthOfMarch says:

    @aw
    Ahhh, yes. Probability = kebarangkalian. Hehehe.

    If that figure is correct, it’s once in 149M times, not 149K ;-) . No one catch any “balls” in this post yet, is there? Hahahha.

    [edited & updated]
    Apparently, aw has caught the “balls”. *same frequency* ;-)

  15. TenthOfMarch says:

    @aw
    No worries. Your mind is working great — you did caught the “ball” afterall. Hahaha. And your step 1 – 3 sounds good. Based on their previous replies, it’s like their “protocol” or something.

  16. aw says:

    My post was in beta, my technical staff is working on it :)

    Actually it’s amazing that Boss Lepton and freethinker still remember their probabilities!

  17. Boss Lepton says:

    hehehehe there is an entire area on whether 1/10 represents 1 out of 10 cases, and it has resulted in 2 class of statisticians (yes, statisticians also have beliefs like economists on classical or keynesian etc assumptions)

    i am of the agreement that 1/10 represents that if there are 10 incidents, it is EXPECTED that the event will occur once with probability one.

    Read the statement again, looks trivial but has a very deep statistical meaning :D

    anyway yea, hope i’m right hahaha

  18. TenthOfMarch says:

    @Boss Lepton
    Wahhh…this philosophy is seriously getting a little too deep for me. Hahahhaa. I know, it’s like even though it’s a 0.1 chances, doesn’t mean after 10 times one event will happen. Or, maybe the event will happen after less than 10 “tries”. But it’s getting more complicated that way — so I’ll stick to what you suggested.

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