Question

Consider two independent events $E$ and $F$ such that$P(E)=1/4,P(E∪F)=2/5$ and $P(F)=a$.Then,the value of $a$ is

• A. $\dfrac{13}{20}$
• B. $\dfrac{1}{20}$
• C. $\dfrac{1}{4}$
• D. $\dfrac{1}{5}$
• E. $\dfrac{3}{5}$

Answer 1

Answer: (D)

$\dfrac{1}{5}$

Answer 2

Given Data

$P(E)=\dfrac{1}{4},P(E∪F)=\dfrac{2}{5}$

We know that,

$P(E ∪ F) = P(E) + P(F) - P(E ∩ F)$

$P(E ∩ F) = \dfrac{1}{4} + a - \dfrac{2}{5}$---------(1)

Now, $P(E ∩ F) = P(E) × P(F)$

$P(E ∩ F) = (1/4) × a$----------(2)

Now, we can equate (1) and (2) to get the value of $'a’$

$\dfrac{1}{4} × a = \dfrac{1}{4} + a - \dfrac{2}{5}$

$⇒\dfrac{1}{4} × a -a = \dfrac{-3}{20}$

$⇒\dfrac{-3a}{4}=\dfrac{-3}{20}$

$⇒a=\dfrac{1}{5}$ (_Ans)