a coin has two sides. when the coin is flipped, each side appears with probability 1/2.?

Supposed a coin is flipped 8 times. what is the chance that both heads and tails appear an equal number of times?

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  • Amit Y
    Lv 5
    1 decade ago
    Favorite Answer

    The number of ways to flip a coin 8 times: 2^8 = 256

    The number of ways to select 4 times out of 8, when tails appear:

    8! / (4! * 4!) = (5 * 6 * 7 * 8) / (1 * 2 * 3 * 4) =

    = 5 * 6 / (2 * 3) * 7 * (8 / 4) = 5 * 7 * 2 = 70

    The chance is 70 / 256 = 35 / 128 = 0.2734375

  • sd3r
    Lv 7
    1 decade ago

    i agree with 1 in 16.

    look at it this way, flipping a coin 8 times is 2^^8 flips or 256. if a 1 represents heads and a 0 represents tails, you need all the binary numbers between 0 and 255 with exactly four 1's and four 0's. now, whatever place the four 0's appear in the eight possible places, there is only 1 in 16 chance those will be all 0's in every combination of 8 bits.

    so again, i'll go with 1:16.

    people saying 1:2, read the problem, you're wrong.

  • 1 decade ago

    1/16

    What you are trying to find out is the probability of getting 4 heads (or 4 tails). Each time the coin is flipped, there is a 1/2 chance of its being a head. There is a 1/2 chance in each of the first 4 flips. Multiply them together.

  • Anonymous
    1 decade ago

    1 out of 16

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  • 1 decade ago

    From what I see, there are 9 scenarios:

    ~ 8 heads, no tails

    ~ 7 heads, 1 tail

    ~ 6 heads, 2 tails

    ~ 5 heads, 3 tails

    ~ 4 heads, 4 tails <--- the one you want

    ~ 3 heads, 5 tails

    ~ 2 heads, 6 tails

    ~ 1 head, 7 tails

    ~ no head, 8 tails

    So it's 1/9 chance.

    I may be wrong, but somehow I don't really get the "1/2 no matter how many flips" theory.

  • 1 decade ago

    the odds are the same for each flip.

    even if you flipped the coin 100 times and it was tails every time, your next flip would still have a 1/2 chance

  • 1 decade ago

    1/16

  • 1 decade ago

    1/2

    .

  • 1 decade ago

    2/8

  • 1 decade ago

    provided the coin spins a lot in flight the odds are equal, in the game of two up, flat or non spinning coins are not permitted as the odds can be manipulated depending on which of the coin faces are placed upwards on the kip (piece of wood slat that is used)

    Source(s): two up, very popular gambling game.
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