how do i solve this probability question?

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How many ways can you order the $b+g$ people such that the $i$-th person is a girl?

Clearly, there are $g$ ways to choose a girl to place in the $i$-th position. There are then $(b+g-1)!$ ways to arrange the rest of the people. Therefore, $$P(G_i)=\frac{g\cdot(b+g-1)!}{(b+g)!}=\frac{g}{b+g}.$$

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idknuttin
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Updated on October 22, 2022

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  • idknuttin
    idknuttin about 1 year

    can someone explain step by step how to solve this?

    A group of individuals containing b boys and g girls is lined up in random order; that is, each of the (b + g)! permutations is assumed to be equally likely. Let Gi be the event the i-th person is a girl. Find P(Gi).

    • callculus42
      callculus42 about 8 years
      The probability that a girl is on the first position is just $\frac{g}{b+g}$ This probability is equal for all positions.
    • idknuttin
      idknuttin about 8 years
      thanks, that's an easy way of looking at it