Verified Solution • 2025–26 Session moderate

QJEEM20Mac758: JEE Main 2020 Mathematics - Class 12 JEEM20Mac758 Solution: Let A and B be two independent events such that P(A) = and P(B) …

Let A and B be two independent events such that
P(A) = 13{1 \over 3} and P(B) = 16{1 \over 6} .
Then, which of the following is TRUE?

Multiple Choice Options

  • A P(AA∪B)=14P\left( {{A \over {A \cup B}}} \right) = {1 \over 4}
  • B P(AB)=23P\left( {{A \over B}} \right) = {2 \over 3}
  • C P(A′B′)=13P\left( {{{A'} \over {B'}}} \right) = {1 \over 3}
  • D P(AB′)=13P\left( {{A \over {B'}}} \right) = {1 \over 3}

Step-by-Step Verified Solution

Given P(A) = 13{1 \over 3} and P(B) = 16{1 \over 6}

A and B are independent

So P(A ∩\cap B) = 13×16{1 \over 3} \times {1 \over 6} = 118{1 \over {18}}

P(A ∪\cup B) = P(A) + P(B) – P(A ∩\cap B)

= 13{1 \over 3} + 16{1 \over 6} - 118{1 \over {18}}

= 49{4 \over 9}

P(AB′)P\left( {{A \over {B'}}} \right)

= P(A∩B′)P(B′){{P\left( {A \cap B'} \right)} \over {P\left( {B'} \right)}}

= P(A)−P(A∩B)1−P(B){{P\left( A \right) - P\left( {A \cap B} \right)} \over {1 - P\left( B \right)}}

= 13−1181−16{{{1 \over 3} - {1 \over {18}}} \over {1 - {1 \over 6}}} = 13{{1 \over 3}}

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