Let E and F be the events with PE-35- PF-310- PE- F-15- Are E and F independent -

Given P(E)=35 and P(F)=310,P(E∩ F)= 15 ∴ P(E)× P(F)=35×310=950 ∵ 15≠950 ⇒ P(E∩ F)≠ P(E) × P(F) Therefore, E and F are not ...

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Standard X

Mathematics

Addition Theorem of Probability for 2 Events

Let E and F b...

Question

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

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Solution

Given $P (E) = \frac{3}{5}$ and $P (F) = \frac{3}{10}, P (E \cap F) = \frac{1}{5}$

$∴ P (E) \times P (F) = \frac{3}{5} \times \frac{3}{10} = \frac{9}{50}$

$∵ \frac{1}{5} \neq \frac{9}{50}$

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

Therefore, $E$ and $F$ are not independent.

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Let E and F be the events with P(E)=35,P(F)=310,P(E∩F)=15. Are E and F independent ?

Given P(E)=35 and P(F)=310,P(E∩F)=15∴P(E)×P(F)=35×310=950∵15≠950⇒P(E∩F)≠P(E)×P(F)Therefore, E and F are not independent.

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

Given $P (E) = \frac{3}{5}$ and $P (F) = \frac{3}{10}, P (E \cap F) = \frac{1}{5}$

$∴ P (E) \times P (F) = \frac{3}{5} \times \frac{3}{10} = \frac{9}{50}$

$∵ \frac{1}{5} \neq \frac{9}{50}$

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

Therefore, $E$ and $F$ are not independent.