A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit.

Discussion in 'Calculator Requests' started by math_celebrity, Jan 27, 2022.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit.

    At least 1 female rabbit means we must have a female rabbit
    First, we calculate the probability of 0 females

    A rabbit can be either male or female with equal probabilities of 1/2 or 0.5.

    Since each birth is independent, we can multiply to get the probability of all males:
    P(MMMMMMMMMM) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2
    P(MMMMMMMMMM) = 1/1024

    Then, we subtract this probability from 1 to get the probability of at least one female:
    P(At least one F) = 1 - 1/1024

    Since 1 = 1024/1024, we have:
    P(At least one F) = (1024 - 1)/1024
    P(At least one F) = 1023/1024
     

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