Let E and F be two independent events- The probability that exactly one of them occurs is 11-25 andthe probability that none of them occurs is 2-25-Then P E - F -A- 12-25B- 0-2523C- 20-2513D- 10-25

The correct option is A P(E ⋂ nbsp;F̅) + P(E̅⋂F̅) =11/25 , P(E̅ nbsp;⋂ nbsp;F̅) =2/25 nbsp;⇒ P(E) = 4/5, nbsp;P(F) = 3/5 nbsp; ∴ P(E ⋂ nbsp;F ...

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Byju's Answer

Standard XII

Mathematics

Independent Events

Let E and F b...

Question

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ andthe probability that none of them occurs is $\frac{2}{25}$ .Then $P (E ⋂ F) =$

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$\frac{13}{25}$

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$\frac{8}{25}$

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$\frac{12}{25}$

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Solution

The correct option is D
$\frac{12}{25}$

$P (E ⋂ ¯ F) + P (¯ E ⋂ ¯ F) = \frac{11}{25}$ , $P (¯ E ⋂ ¯ F) = \frac{2}{25}$
$\Rightarrow P (E) = \frac{4}{5}$ , $P (F) = \frac{3}{5}$
$∴ P (E ⋂ F) = P (E) P (F) = \frac{12}{25}$

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Let E and F be two independent events. The probability that exactly one of them occurs is1125 andthe probability that none of them occurs is 225 .Then P(E⋂F)=

The correct option is D P(E⋂¯F)+P(¯E⋂¯F)=1125 , P(¯E⋂¯F)=225 ⇒P(E)=45, P(F)=35 ∴P(E⋂F)=P(E)P(F)=1225

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ andthe probability that none of them occurs is $\frac{2}{25}$ .Then $P (E ⋂ F) =$

The correct option is D
$\frac{12}{25}$

$P (E ⋂ ¯ F) + P (¯ E ⋂ ¯ F) = \frac{11}{25}$ , $P (¯ E ⋂ ¯ F) = \frac{2}{25}$
$\Rightarrow P (E) = \frac{4}{5}$ , $P (F) = \frac{3}{5}$
$∴ P (E ⋂ F) = P (E) P (F) = \frac{12}{25}$