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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
Two events A and B have probability 0.28 and 0.55 respectively. The probability that A and B occur simultaneously is 0.14. Find the probability that neither A nor B occurs
  • A
    0.39
  • B
    0.41
  • C
    0.4
  • ✓
    0.31
✓

Answer

Correct option: D.
0.31
(D)
$\begin{array}{l} P ( A )=0.28, P ( B )=0.55, P ( A \cap B )=0.14 \\ P \left( A ^{\prime} \cap B ^{\prime}\right)= P \left[( A \cup B )^{\prime}\right]=1- P ( A \cup B ) \\ =1-[ P ( A )+ P ( B )- P ( A \cap B )] \\ =1-(0.28+0.55-0.14)=0.31\end{array}$

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