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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability2 Marks
Question
Let E and F be events with $\text{P}(\text{E})=\frac{3}{5},\ \text{P}(\text{F})=\frac{3}{10}\ \text{and}\ \text{P}(\text{E}\cap\text{F})=\frac{1}{5}.$ Are E and F independent?
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Answer

It is given that $\text{P}(\text{E})=\frac{3}{5},\ \text{P}(\text{F})=\frac{3}{10},\ \text{and}\ \text{P}(\text{EF})=\text{P}(\text{E}\cap\text{F})=\frac{1}{5}$$\text{P}(\text{E}).\text{P}(\text{F})=\frac{3}{5}\cdot\frac{3}{10}=\frac{9}{50}\neq\frac{1}{5}$
$\Rightarrow\text{P}(\text{E}).\text{P}(\text{F})\neq\text{P}(\text{EF})$
Therefore, E and F are not independent.

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