CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Mr. Dupont is a professional wine taster. When given a French wine, he will identify it with probability $$0.9$$ correctly as French and will mistake it for a Californian wine with probability $$0.1$$. When given a Californian wine, he will identify it with probability $$0.8$$ correctly as Californian and will mistake it for a French wine with probability  $$0.2$$. Suppose that Mr. Dupont is given ten unlabelled glasses of wine, three with French and seven with Californian wines. He randomly picks a glass, tries the wine and solemnly says : "French". The probability that the wine he tasted was Californian, is nearly equal to


A
0.14
loader
B
0.24
loader
C
0.34
loader
D
0.44
loader

Solution

The correct option is C $$0.34$$
Given,There are 7 californian wine glasses and 3 french wine glasses.
The probability of selecting French wine glass, $$P(FG)=\frac{3}{10}$$
The probability of selecting California wine glass, $$P(CG)=\frac{7}{10}$$ When given french wine,
The probability of Dupont to say correctly as french wine, $$P(F)=0.9$$ When given french wine,
The probability of Dupont to say wrongly as Californian wine, $$P(\overline F)=0.1$$ When given Californian wine,
The probability of Dupont to say correctly as Californian wine, $$P(F)=0.8$$ When given Californian wine,
The probability of Dupont to say wrongly as french wine, $$P(\overline C)=0.2$$$$\therefore$$
The probability that Dupont says selected glass as French wine, $$P(A)=$$The probability of selecting french wine glass and will say $$correctly$$ as $$french$$ wine $$+$$ Probability of selecting $$californian$$ wine glass and saying $$wrongly$$ it as $$French$$ wine. $$=P(FG)*P(F)+P(CG)*P(\overline C)$$
$$=\displaystyle\frac{3}{10}*0.9+\displaystyle\frac{7}{10}*0.2=0.041$$
$$\therefore$$ The probability that Dupont says selected glass as French wine Given it as Californian=$$\displaystyle\frac{P(CG)*P(\overline C)}{P(A)}=\displaystyle\frac{(\frac{7}{10}*0.2)}{0.41}=0.341$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image