Q84 / 180 · KCET 2021 · Mathematics

If $P(A)=0.59, P(B)=0.30$ and $P(A \cap B)=0.21$ then $P\left(A^{\prime} \cap B^{\prime}\right)$ is equal to

  • A
    $0.11$
  • B
    $0.38$
  • Correct answer
    C
    $0.32$
  • D
    $0.35$

Solution

Given, $P(A)=0.59, P(B)=0.30$ and $P(A \cap B)=0.21$ $\begin{aligned} P\left(A^{\prime} \cap B^{\prime}\right) &=1-P(A \cup B) \quad[\therefore \text { De Morgan's law }] \\ =& 1-[P(A)+P(B)-P(A \cap B)] \\ =& 1-[0.59+0.30-0.21] \\ =& 1-[0.89-0.21] \\ =& 1-0.68=0.32 \end{aligned}$

Hence, the correct answer is option: 'C'.

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