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Probability

Discussion in 'General Electronics Discussion' started by ramit36, Oct 10, 2012.

  1. ramit36

    ramit36

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    0
    Oct 9, 2012
    Earlier in the morning I was thinking about the example of an experiment of tossing an unbiased coin and getting a head was an event in that.

    So, according to the definition of the probability the answer will be

    Total number of favorable outcomes = 1
    Total number of outcomes = 2
    Probability of getting a head = ½

    Now, consider if we toss the coin for 100 times then what will happen to the probability of getting a head?

    Tossing a coin for 100 times can give maximum of 100 heads if considered that every time it happened by miracle or something like that. But then total number of outcomes will be 200 (each time there are two outcomes possible). So, if now we calculate the probability o f getting a head then

    Total number of favorable outcomes = 100
    Total number of outcomes = 200
    Probability of getting a head = 100/200 = 1/2 (again same, and this is what is supposed to happen)

    Anybody who want to say anything on this your welcome..
     
  2. GreenGiant

    GreenGiant

    830
    5
    Feb 9, 2012
    While your math is correct you are a little flawed...

    You are saying "total number of outcomes" when you mean "total possible outcomes"
    if you toss a coin once the total number of outcomes is 1, you will only have 1 result, now if you look at the heads as the favorable outcome, then you have 1 favorable outcome out of 2 possible outcomes
    that is where you get the 1/2

    if you toss the coin 100 times you will have again 1 favorable outcome out of 2 possible outcomes which gives you 1/2, now for 100 tosses you would simply multiply 100 x (1/2) = 50 so therefor the probability of getting heads out of 100 tosses is 50/100 or 1/2
    you have to look at it like this.... favorable outcomes/total number of tosses
     
  3. ramit36

    ramit36

    17
    0
    Oct 9, 2012
    First of all thank you very much for the reply. And all i can say right now is that i am all confused. What you explained i mean the way you explained it, your way of calculation and everything is making sense to me and what i did is everything that was going on in my head at that moment i just wrote it down in word file and then pasted here. So, at last i want to say that i need some time to figure this out and what exactly is happening or how exactly this probability calculation works. And thanks to you once again, once i will get the clear idea about this, i will reply.
     
  4. BobK

    BobK

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    1,643
    Jan 5, 2010
    The number of possible outcomes of tossing a coin 100 times is 2^100. The number of possible outcomes that have no heads is 1 (i.e. every toss must be a tail). So the probablility of having at least 1 head is that same as 1 - the probability of having all tails. The probability of having all tails is 1 / (2 ^ 100). So the probabilty of having at least 1 head in 100 tosses is 1 - 1 / (2 ^ 100) or 0.99999999999999999999999999999921.

    Bob
     
  5. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

    25,175
    2,690
    Jan 21, 2010
    Welcome to permutations and combinations (which is incidentally something to Google for enormous amounts of explanation)
     
  6. Raven Luni

    Raven Luni

    798
    7
    Oct 15, 2011
    You're all a bunch of tossers :p *runs away very fast*
     
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