If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5},P\left( \overline{A} \cup \overline{B} \right) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$, then$P(A)$ equals

Question

Dr. Abubacker · Accepted Answer

(c)
Given, $P\left( \overline{A} \cup \overline{B} \right) = P(\overline{A \cap B}) = \frac{7}{10}$
Since,$P(A \cap B) + P(\overline{A \cap B})$=1
$\Rightarrow P(A \cap B) = 1 - \frac{7}{10} = \frac{3}{10}$
Also, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow \frac{4}{5} = P(A) + \frac{2}{5} - \frac{3}{10}$
$\Rightarrow P(A) = \frac{4}{5} - \frac{2}{5} + \frac{3}{10}$
$= \frac{2}{3} + \frac{3}{10} = \frac{7}{10}$

Q. If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5},P\left( \overline{A} \cup \overline{B} \right) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$, then$P(A)$ equals

Explanation

Reviewed by Dr. Abubacker

Want more practice?