Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02,0.03 and 0.05 , it fails to rise. In the restaurant where they work, X bakes 50 %, Y bakes 30 % and Z bakes 20 % of cakes. What is the proportion of

Question

Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02,0.03 and 0.05 , it fails to rise. In the restaurant where they work, X bakes 50 %, Y bakes 30 % and Z bakes 20 % of cakes. What is the proportion of failures caused by X ?

Quantrex Academy · Accepted Answer

Correct answer: B. 10 29

From question, we have P(F X)=0.02, P(F Y)=0.03, P(F Z)=0.05 and P(F)=P(X) P(F X)+P(Y) P(F Y) array ll & =0.5 0.02+0.3 0.03+0.2 0.05 & +P(Z) P(F Z) = & 0.01+0.009+0.01=0.029 array Now, aligned & P(X F)=P(X) P(F X)=0.5 0.02=0.01 . & P(X F)= P(X F) P(F) = 0.01 0.029 = 10 29 aligned

Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02,0.03 and 0.05 , it fails to rise. In the restaurant where they work, X bakes 50 %, Y bakes 30 % and Z bakes 20 % of cakes. What is the proportion of failures caused by X ?

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