Case study problem probability 2 chapter 13 class 12

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Case study Chapter 13 (Probability)

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

    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.

Case study problem probability

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

(a) 7/10                    (b) 4/5

(c) 3/5                       (d) 1/5

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

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

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

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

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

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

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

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

(c) 3/10                         (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) 2/3                            (b) 3/5

(c) 3/7                             (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

(i) Answer (c)

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

⇒ P(A/X) = 60/100 = 3/5

(ii) Answer (c)

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

= P(X)×P(A/X) = 1/3×60/100

= 1/3×3/5 = 1/5

(iii) Answer (a)

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

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

(iv) Answer (b)

The total probability that a farmer believe in new technology

= P(X)×P(A/X) + P(Y)×P(A/Y) + P(Z)×P(A/Z)

= 1/3×60/100 + 1/3×70/100 + 1/3×80/100

=\frac{1}{3}\times(\frac{60+70+80}{100})

= \frac{1}{3}\times \frac{210}{100}

= \frac{7}{10}

(v) Answer (d) 

P(farmer believe in new technology of agriculture, the probability that the farmer belongs mohalla ‘B’)

\Rightarrow P(Y/A) = \frac{P(Y)\times P(\frac{A}{Y})}{P(X)\times P(\frac{A}{X})+P(Y)\times P(\frac{A}{Y})+P(Z)\times P(\frac{A}{Z})}

=\frac{\frac{1}{3}\times \frac{70}{100}}{\frac{1}{3}\times \frac{60}{100}+\frac{1}{3}\times \frac{70}{100}+\frac{1}{3}\times \frac{80}{100}}

= \frac{\frac{1}{3}\times \frac{70}{100}}{\frac{1}{3}\times \frac{210}{100}}

= \frac{7}{30}\times \frac{10}{7}= \frac{1}{3}

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