Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.9k views
in Probability Distribution by (15 points)
edited by

There are two shops in a village market named A and B. In  A 30 tin of pure mustard oil, 40 tin of adulterated mustard oil while in B tin of pure mustard oil, 60 tin of adulterated mustard oil are there Mr .Gautam wants to buy one tin of mustard oil from any store selected at random.

Based on the above information, answer the following questions : 

Find the conditional probability that an adulterated mustard oil tin is bought given that 

(i) store A is selected at random 

(ii) store  B is selected at random

Please log in or register to answer this question.

1 Answer

0 votes
by (42.1k points)

Let 

A =  selection of shop A 

B =  selection of shop B

E =  buying of adulterated mustard oil

\(\therefore P(A) = P(B) = \frac12\) 

\(P\left(\frac EA\right) = \frac{40}{30 + 40} = \frac{40}{70} = \frac47\) 

\(P\left(\frac EB\right) = \frac{60}{50 + 60} = \frac{60}{110} = \frac6{11}\)

(i) Probability of event of selection shop A when given that adulterated mustard oil bought 

\(= P\left(\frac AE\right) =\frac{P(\frac EA)P(A)}{P(\frac EA) P(A) + P(\frac{E}{B})P(B)}\)

\(= \cfrac{\frac47 \times \frac12}{\frac47\times\frac12 + \frac6{11}\times \frac12} \)

\(=\cfrac{\frac12\left(\frac47\right)}{\frac12 \left(\frac47 + \frac6{11}\right)} \)

\(= \cfrac{\frac47}{\frac{44+42}{77}}\)

\(= \frac47 \times \frac{77}{86}\)

\(= \frac{2\times11}{43}\)

\( = \frac{22}{43}\)

(ii) Probability of event of selection shop B when given that adulterated mustard oil bought 

\(= P\left(\frac BE\right) =\frac{P(\frac EB)P(B)}{P(\frac EA) P(A) + P(\frac{E}{B})P(B)}\)

\(= \cfrac{\frac6{11} \times \frac12}{\frac47\times\frac12 + \frac6{11}\times \frac12} \)

\(= \cfrac{\frac6{11} \times \frac12}{\frac12 \left( \frac47 + \frac6 {11}\right)}\)

\(= \frac{6}{11} \times \frac{77}{86}\)

\( = \frac{3 \times 7}{43}\)

\( = \frac{21}{43}\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...