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coward
coward asked in Science & MathematicsMathematics · 7 years ago

probabilty question?

1. A bin of nuts is mixed, containing 30% 1/2 in.nuts and 70% 9/16 in.nuts. A bin of bolts has 40% 1/2 in.bolt, 60% 9/16 in.bolts. Suppose that one bolt and one nut are selected(independently and at random) from two bins.

(a) what is the conditional probability that the nut is a 9/16 in.nut, given that the nut and bolt match?

2. At final inspection of certain integrated circuit chips, 20% of the chips are in fact defective. An automatic testing device does the final inspection. Its characteristics are such that 95% of good chips test as good. Also, 10% of the defective chips test as good.

(a) What is the probability that the next chip is good and tests as good?

(b) what is the probability that the next chip tests as good?

(c) what is the (conditional) probability that the next chip that tests as good is in fact good?

1 Answer

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  • M3
    Lv 7
    7 years ago
    Favorite Answer

    1/

    P[matching 9/16 "] = .7*.6 = .42

    P[matching 1/2 "] = .3*.4 = .12

    by Bayes,

    P[nut is 9/16 " | matching] = .42/(.42+.12) = 42/56 = 3/4 <-----

    2/

    a) P[good & tests good] = .8*.95 = .76 <------

    b) P[bad & tests good] = .8*.95 + .2*.1 = .78 <------

    c) P[good | tests good] = .76/.78 = 38/39 <-----

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