math/statistics

From a shipment of 65 transistors, 4 of which are defective, a sample of 6 transistors is selected at random.
(a) In how many different ways can the sample be selected?
ways

(b) How many samples contain exactly 3 defective transistors?
166320 samples

(c) How many samples do not contain any defective transistors?
samples

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  2. 👎 0
  3. 👁 1,359
  1. Hypergeometric distribution applies to a limited population from which a sample is drawn without replacement.

    Here we assume all defectives are identical, so are undefectives.
    D=4 (defective)
    U=65-4=61 (undefective) =>
    S=U+D=65=size of population=65
    d=defectives selected
    u=undefectives selected =>
    s=u+d=size of sample=6
    C(n,r)=n!/(r!(n-r)!)=number of possible combinations selecting r from n objects.

    (a)
    Number of ways
    =C(S,s)
    =C(65,6)
    =82598880

    (b)
    u=3, d=3
    Number of samples with exactly 3 defectives
    =C(D,d)*C(U,u)
    =C(4,3)*C(61,3)
    =143960

    (c)
    u=6
    d=0
    Number of samples without defectives
    =C(D,d)*C(U,u)
    =C(4,0)*C(61,6)
    =55525372

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    2. 👎 0
  2. From a shipment of 70 transistors, 4 of which are defective, a sample of 5 transistors is selected at random.

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    2. 👎 0

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