Question14 C1 poin) n left to The circuit below operates provided there is a pat

Question

Question14 C1 poin) n left to The circuit below operates provided there is a path of functiona right. The probability of each component functioning corecly diagram and the components function independently, What is e circuit functioning correctly? ices from lent is shown in the What is the probability of the 0.70.7 0.8 0.8 Question 15 (1 point) A company buys microchips from three supplies (I, II, and III). Supply I has a record ofproviding microchips that contain 600 defectives; Supply II has defective rate of 5%, and Supply III has a defective rate of 2%. Suppose that 25%, 34%, and 41% of the current supply came from Supplies I, II, and III, respectively. (a) If a microchip is selected at random from this supply, what is the probability that it is defective? b) If a randomly selected microchip is defective, what is the probability that it came from Supply 11?

Explanation / Answer

1.)

Given that:

A,B,C,D,E are independent

Let's Say that path having A and B is X

and path having C, D and E is Y

Path X is functional only when A nd B both are functional

So, Probability of path X being functional is,

P(X) = P(A and B both functional) = P(A) * P(B) = 0.7 * 0.7 = 0.49

Similarly, Probability of path Y being functional is,

P(Y) = 0.8 * 0.8 * 0.8 = 0.512

Path will be functional only when either path X or Y is functional

So, P(either X or Y works) = P(X works) + P(Y works) - P( X and Y works)

P( X and Y works) = P(X) * P(Y) [ Since all A,B,C,D and E are independent)

P( X and Y works) = 0.49 * 0.512 = 0.25

So, P(either X or Y works) = 0.49 + 0.512 - 0.25

P(either X or Y works) = 0.752

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