Asystem contains ewo components A and B, connected in series. Assume A and funct

Question

Asystem contains ewo components A and B, connected in series. Assume A and function independently. Foe the system to function, both components must function. a) If the probability tha ails is 005 and the probability that B faills Is 0.03, find the probability that the sytem functions probability that the system functions Is 0.907 perallel.ie for the system to function either A or B must functioni b I both A and B have probability po failing, what must the value op be so that the ) How will your result in part ) change if the two components were connected in

Explanation / Answer

Prob4:

Let M shows the car sold has medium size engine, S shows the car sold has small size engine and L shows the car sold has large size engine.

So we have

P(M) = 0.35, P(S) = 0.45, P(L) = 0.20

Let F shows the event car fail emission test. So

P(F|M) = 0.12, P(F|S) = 0.10, P(F|L) = 0.15

(a)

By the law of total probability, the probability that car fail emission is

P(F) = P(F|M)P(M)+P(F|S)P(S)+P(F|L)P(L) = 0.12 * 0.35 + 0.10 * 045 + 0.15* 0.20 =0.117

(b)

P(S|F) = [ P(F|S)P(S) ] / P(F) = [0.10*0.45] / 0.117 = 0.3846

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