A lot contains 50 defective and 50 non defective b

Question

A lot contains 50 defective and 50 non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events A, B, C are defined asA = (the first bulb is defective)B = (the second bulb is non – defective) C = (the two bulbs are both defective or both non defective)Determine whether(i) A, B, C are pair wise independent(ii) A, B, C are independent.

Jitender Pal · Accepted Answer

Hello Student,Please find the answer to your questionLet S = defective and Y = non defective. Then all possible outcomes are {XX, XY, YX, YY}Also P (XX) = 50/100 x 50/100 = 1/4,P (XY) = 50/100 x 50/100 = 1/4,P (YX) = 50/100 x 50/100 = 1/4,P (YY) = 50/100 x 50/100 = 1/4Here, A =XX &cup; XY; B = XY &cup; YY; C = XX &cup; YY&there4; P (A) = P (XX) + P (XY) = 1/4 + 1/4 = 1/2&there4; P (B) = P (XY) + P (YX) = 1/4 + 1/4 = 1/2P (C) = P (XX) + P (YY) = 1/4 + 1/4 =1/2Now, P (AB) = P (XY) = 1/4 = P (A). P (B)&there4; A and B are independent events.P (BC) = P (YX) = 1/4 = P (B). P (C)&there4; B and C are independent events.P (CA) = P (XX) = 1/4 = P (C). P (A)&there4; C and A are independent events.P (ABC) = 0 (impossible event)&ne; P (A) P (B) P (C)&there4; A, B, C are dependent events,Thus we can conclude that A, B, C are pair wise independent bet A, B, C are dependent events.ThanksJitender PalaskIITians Faculty

Algebra> A lot contains 50 defective and 50 non de...

Hrishant Goswami , 10 Years ago

Jitender Pal

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Hrishant Goswami , 10 Years ago

Jitender Pal

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