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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Choose the correct answer from the given four options.
If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:
  • A
    $\frac{4}{15}$
  • B
    $\frac{8}{45}$
  • C
    $\frac{1}{3}$
  • D
    $\frac{2}{9}$
✓

Answer

  1. $\frac{2}{9}$

Solution:

Since A and B are independent events, A' And B' are aslo independent.

$\therefore\text{P}(\text{A}'\cap\text{B}')=\text{P}(\text{A})\cdot\text{P}(\text{B})$

$=\big[1-\text{P}(\text{A})\big]\big[1-\text{P}(\text{B})\big]$

$=\Big(1-\frac{3}{5}\Big)\Big(1-\frac{4}{9}\Big)$

$=\frac{2}{5}\cdot\frac{5}{9}=\frac{2}{9}$

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