# Case study Chapter 13 (Probability)

Read the following and answer the question(Case study problem probability 2 chapter 13 class 12)

Â  Â  in a village there are three mohallas A, B and C. In A, 60% farmers believe in new technology of agriculture, while in B, 70% and in C, 80%. A farmer is selected at random from village.

(i) The conditional probability that a farmer believe in new technology if he belongs mohalla A is

(a) 7/10Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 4/5

(c) 3/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 1/5

(ii) The probability that mohalla A selected and selected farmer believed in new technology of agriculture isÂ

(a) 2/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 3/5

(c) 1/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) None of these

(iii) The conditional probability that a farmer believe in new technology of agriculture if he belongs mohalla C is

(a) 4/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 3/5

(c) 1/5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 2/5

(iv) The total probability that a farmer believe in new technology of agriculture is

(a) 2/7Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 7/10

(c) 3/10Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 8/10

(v) District agriculture officer select a farmer at random in village and he found that selected farmer believe in new technology of agriculture, the probability that the farmer belongs mohalla ‘B’ is

(a) 2/3Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 3/5

(c) 3/7Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 1/3

Solution: Let X = Selecting mohalla ‘A’

Y = Selecting mohalla ‘B’

Z = Selecting mohalla ‘C’

A = Farmer believe in new technology.

P(X) = 1/3, P(Y) = 1/3, P(Z) = 1/3

P(A/X) = 60/100, P(A/Y) = 70/100, P(A/Z) = 80/100

P(a farmer believe in new technology if he belongs mohalla A )

â‡’ P(A/X) = 60/100 = 3/5

P(mohalla A selected and selected farmer believed in new technology)

= P(X)Ã—P(A/X) = 1/3Ã—60/100

= 1/3Ã—3/5 = 1/5

P(a farmer believe in new technology of agriculture if he belongs mohalla C )

= P(A/Z) = 80/100 = 4/5

The total probability that a farmer believe in new technology

= P(X)Ã—P(A/X) + P(Y)Ã—P(A/Y) + P(Z)Ã—P(A/Z)

= 1/3Ã—60/100 + 1/3Ã—70/100 + 1/3Ã—80/100