What are the odds of a 1/8192 chance happening twice within 30 attempts?

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What would be the odds of this happening? There is a 1/8192 chance of finding a shiny pokemon. So what are the odds of finding 2 within 30 attempts/tries? I wouldn’t know how to calculate that so if anyone could do that, because I am just curious.

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? Best Answer

  • This follows the binomial distribution.
    The odds of finding 1 Shiny Pokémon in the wild is 1/8192.

    The number of attempts made here is 30.
    So n = 30.
    Probability of finding a shiny Pokémon is 1/8192.
    So p = 1/8192
    Probablity of not finding a shiny Pokémon is 8191/8192.
    So q = 8191/8192

    The probability of finding 2 shiny Pokémon in 30 attempts is given by
    P(X=2)
    = 30C2 x p^2 x q^(30-2)
    = 435 x (1/8192)^2 x (8191/8192)^28
    = 6.45 x 10^-6

    There’s a 6.45 in 1 million chance of getting 2 shinies in 30 attempts.

    I myself have seen just 1 shiny Pokémon in the wild after playing about 150 hours on Pokémon FireRed.

  • (1/8192)^2(8191/8192)^28
    In other words, astronomical.

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