A coin is tossed twice. If events $A$ and $B$ are defined as :$A =$ head on first toss, $B = $ head on second toss. Then the probability of $A \cup B = $
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{1}{8}$
$\frac{3}{4}$
A party of $23$ persons take their seats at a round table. The odds against two persons sitting together are
If $A$ and $B$ are any two events, then $P(A \cup B) = $
Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is
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 $)$
Two aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $l$ and $II$ scoring a hit correctlyare $0.3$ and $0.2,$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is