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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
If A and B are two events such that $\text{P}(\text{A})=\frac{1}{4},\ \text{P}(\text{B})=\frac{1}{2}\ \text{and}\ \text{P}(\text{A}\cap\text{B})=\frac{1}{8},$ find P(not A and not B).
✓

Answer

It is given that, $\text{P}(\text{A})=\frac{1}{2}\ \text{and}\ \text{P}(\text{A}\cap\text{B})=\frac{1}{8}$P(not on A and not on B) $=\text{P}(\text{A}'\cap\text{B}')$
P(not on A and not on B) $=\text{P}((\text{A}\cup\text{B}))'\left[\text{A}'\cap\text{B}'=(\text{A}\cup\text{B})'\right]$
$=1-\text{P}(\text{A}\cup\text{B})$
$=1-\left[\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})\right]$
$=1-\Bigg[\frac{1}{4}+\frac{1}{2}-\frac{1}{8}\Bigg]$
$=1-\frac{5}{8}$
$=\frac{3}{8}$

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