If $A$ and $B$ are two independent events, then the probability of occurrence of at least one of $\mathrm{A}$ and $\mathrm{B}$ is given by $1 -\mathrm{P}\left(\mathrm{A}^{\prime}\right) \mathrm{P}\left(\mathrm{B}^{\prime}\right)$
Three persons $P, Q$ and $R$ independently try to hit a target . If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by $P$ or $Q$ but not by $R$ is
For an event, odds against is $6 : 5$. The probability that event does not occur, is
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that One of them is black and other is red.
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 $)$