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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Probability

NDA 2020 · Mathematics · Probability

Three cooks X, Y and Z bake a special kind of cake, and with...

Three cooks X,YX, Y and ZZ bake a special kind of cake, and with respective probabilities 0.02,0.030.02,0.03 and 0.05 , it fails to rise. In the restaurant where they work, XX bakes 50%,Y50 \%, Y bakes 30%30 \% and ZZ bakes 20%20 \% of cakes. What is the proportion of failures caused by XX ?

Options

  1. A929\frac{9}{29}
  2. B1029\frac{10}{29}
  3. C1929\frac{19}{29}
  4. D2829\frac{28}{29}

Correct answer

B. 1029\frac{10}{29}

Step-by-step solution

From question, we have P(F∣X)=0.02,P(F∣Y)=0.03,P(F∣Z)=0.05P(F \mid X)=0.02, P(F \mid Y)=0.03, P(F \mid Z)=0.05 and P(F)=P(X)⋅P(F∣X)+P(Y)⋅P(F∣Y)P(F)=P(X) \cdot P(F \mid X)+P(Y) \cdot P(F \mid Y)=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\begin{array}{ll} & \\ =0.5 \times 0.02+0.3 \times 0.03+0.2 \times 0.05 & +P(Z) \cdot P(F \mid Z) \\ = & 0.01+0.009+0.01=0.029 \end{array}Now,Now,P(X∩F)=P(X)⋅P(F∣X)=0.5×0.02=0.01. and ∴P(X∣F)=P(X∩F)P(F)=0.010.029=1029\begin{aligned}& P(X \cap F)=P(X) \cdot P(F \mid X)=0.5 \times0.02=0.01 . \\ \text{ and } \therefore P(X \mid F)=\frac{P(X \cap F)}{P(F)}=\frac{0.01}{0.029}=\frac{10}{29}\end{aligned}$$
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