An electrical engineer has on hand two boxes of resistors, with four resistors i

Question

An electrical engineer has on hand two boxes of resistors, with four resistors in each box. The resistors in the first box are labeled 10 ohms, but in fact their resistances are 9, 10, 11, and 12 ohms. The resistors in the second box are labeled 20 ohms, but in fact their resistances are 18, 19, 20, and 21 ohms. The engineer chooses one resistor from each bock and determines the resistance of each. Let A be the event that the first resistor has a resistance greater than 10, let B be the event that the second resistor has a resistance less than 19, and let C be the event that the sum of the resistances is equal to 28. Find a sample space for this experiment, and specify the subsets corresponding to events A, B, and C. a) A: b) B: c) C: d) Find B union C e) Find A intersection B^C f) Is it possible for the events A and B to both occur? g) How about B and C? h) How about A and C? i) Which pair of events if mutually exclusive if any?

Explanation / Answer

(a) A = (11, 18) , (11, 19), (11, 20) , (11, 21), (12 18) , (12, 19), (12, 20) , (12, 21)

(B) B = (9, 18) , (10, 18), (11, 18) , (12, 18)

(C) C = (9,19) , (10,18)

(D) Find B U C = (10,18)

(E) A B C = (11, 19),(11, 20) , (11, 21), (12, 19), (12, 20) , (12, 21)

(F) Yes it is possible for events A and B both occur i.e (11,18) , (12,18)

(G) yes B and C can also occur i.e. (10,18)

(H) No A and C can't occur simultanously.

(I) A and C are mutually exclusive.

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