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Math Help - Probability Question

  1. #1
    Junior Member
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    Probability Question

    Hi everyone,

    I am having some trouble getting this question, because it is not a style I have done before.

    In a large population, people are one of three genetic types: A, B, C: 30% are type A, 60% Type B, and 10% Type C. The probability a person carries another gene miking them susceptible for a disease is 0.05 for A, 0.04 for B, and 0.02 for C.

    If ten unrelated persons are selected, what is the probability at least one is susceptible for the disease?

    The answer is 0.342
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  2. #2
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    Re: Probability Question

    Hello, KelvinScale!

    In a large population, people are one of three genetic types: A, B, C:
    . . 30% are Type A, 60% are Type B, and 10% are Type C.

    The probability a person carries certain gene making them susceptible for a disease
    . . is 0.05 for A, 0.04 for B, and 0.02 for C.

    If ten people are selected randomly, what is the probability at least one has that gene?

    30% of the population are Type A; 5% of them have the gene.
    . . We have: . 0.30 \times 0.05 \:=\:0.015
    1.5% of the population are Type A and have the gene.

    60% of the population are Type B; 4% of them have the gene.
    . . We have: . 0.60 \times 0.04 \:=\:0.024
    2.4% of the population are Type B and have the gene.

    10% of the population are type C; 2% of them have the gene.
    . . We have: . 0.10 \times 0.02 \:=\:0.002
    0.2% of population are Type C and have the gene.

    Hence: . 1.5\% + 2.4\% + 0.2\% \:=\:4.1\% of the population has the gene.
    . . and: . 95.9\% do not have the gene.


    Ten people are selected at random.
    We want probability that at least one of them has the gene.

    The opposite of "at least one has the gene" is "none of them has the gene".

    We know that:. P(\text{none has the gene}) \:=\: (0.959)^{10} \:=\:0.657939669 \:\approx\:0.658

    Therefore: . P(\text{at least one has the gene}) \:=\:1 - 0.658 \;=\;0.342

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  3. #3
    Junior Member
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    Re: Probability Question

    Thanks!, I knew it was not as hard as I thought.
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