If $P(A) = P(B) = x$ and $P(A \cap B) = P(A' \cap B') = \frac{1}{3}$, then $x = $

If $P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$ and the events $A$ and $B$ are independent, then $x =$

An electronic assembly consists of two subsystems, say, $A$ and $B$. From previous testing procedures, the following probabilities are assumed to be known :

$\mathrm{P}$ $( A$ fails $)=0.2$

$P(B$ fails alone $)=0.15$

$P(A$ and $ B $ fail $)=0.15$

Evaluate the following probabilities $\mathrm{P}(\mathrm{A}$ fails alone $)$

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If  $E_1$ is the event that die $A$ shows up four, $E_2 $ is the event that die $B$ shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true $?$

Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is