An experiment has $10$ equally likely outcomes. Let $\mathrm{A}$ and $\mathrm{B}$ be two non-empty events of the experiment. If $\mathrm{A}$ consists of $4$ outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is

Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$, the probability that it is found to be red, is

$A$ and $B$ are events such that $P(A)=0.42$,  $P(B)=0.48$ and $P(A$ and $B)=0.16 .$ Determine $P ($ not $A ).$

The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are

A party of $23$ persons take their seats at a round table. The odds against two persons sitting together are

The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject ............ $\%$