Verified Solution • 2025–26 Session moderate

QJEEM22Maa885: JEE Main 2022 Mathematics - Class 12 JEEM22Maa885 Solution: Let and be two events such that and Consider (S1) , (S2) Then :

Let A\mathrm{A} and B\mathrm{B} be two events such that P(B∣A)=25,P(A∣B)=17P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7} and P(A∩B)=19⋅P(A \cap B)=\frac{1}{9} \cdot Consider

(S1) P(A′∪B)=56P\left(A^{\prime} \cup B\right)=\frac{5}{6} ,

(S2) P(A′∩B′)=118P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}

Then :

Multiple Choice Options

  • A Both (S1) and (S2) are true
  • B Both (S1) and (S2) are false
  • C Only (S1) is true
  • D Only (S2) is true

Step-by-Step Verified Solution

P(A/B)=17⇒P(A∩B)P(B)=17P(A/B) = {1 \over 7} \Rightarrow {{P(A \cap B)} \over {P(B)}} = {1 \over 7}

⇒P(B)=79\Rightarrow P(B) = {7 \over 9}

P(B/A)=25⇒P(A∩B)P(A)=25P(B/A) = {2 \over 5} \Rightarrow {{P(A \cap B)} \over {P(A)}} = {2 \over 5}

P(A)=52 . 19=518P(A) = {5 \over 2}\,.\,{1 \over 9} = {5 \over {18}}

S2:P(A′∩B′)=118S2:P(A' \cap B') = {1 \over {18}}

S1:S1: and P(A′∪B)=19+69+118=56.P(A' \cup B) = {1 \over 9} + {6 \over 9} + {1 \over {18}} = {5 \over 6}.

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