Let $\mathrm{E}$ and $\mathrm{F}$ be events with $\mathrm{P}(\mathrm{E})=3 / 5, \mathrm{P}(\mathrm{F})=3 / 10$ and $\mathrm{P}(\mathrm{E} \cap \mathrm{F})=1 / 5$. Are $\mathrm{E}$ and $\mathrm{F}$ independent?

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Let $\mathrm{E}$ and $\mathrm{F}$ be events with $\mathrm{P}(\mathrm{E})=3 / 5, \mathrm{P}(\mathrm{F})=3 / 10$ and $\mathrm{P}(\mathrm{E} \cap \mathrm{F})=1 / 5$ . Are $\mathrm{E}$ and $\mathrm{F}$ independent?

CBSE | Maths | NCERT | Probability

Let $\mathrm{E}$ and $\mathrm{F}$ be events with $\mathrm{P}(\mathrm{E})=3 / 5, \mathrm{P}(\mathrm{F})=3 / 10$ and $\mathrm{P}(\mathrm{E} \cap \mathrm{F})=1 / 5$ . Are $\mathrm{E}$ and $\mathrm{F}$ independent?

Solution:

Given: $P(E)=3 / 5, P(F)=3 / 10$ and $P(E \cap F)=1 / 5$
Evaluating the value of parameter & comparing with given,

$P(E) . P(F)=3 / 5 \times 3 / 10=9 / 50 \neq 1 / 5$

$\Rightarrow P(E \cap F) \neq P(E) . P(F)$

Therefore, $\mathrm{E}$ and $\mathrm{F}$ are not independent events.

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