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
One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?
$E:$ ' the card drawn is a king and queen '
$F:$ ' the card drawn is a queen or jack '
Let $A$ and $B$ be two events such that $P\,(A) = 0.3$ and $P\,(A \cup B) = 0.8$. If $A$ and $B$ are independent events, then $P(B) = $
A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If $E$ is the event that a number greater than or equal to $4$ occurs on a single toss of the die then $P(E)$ is equal to
A die marked $1,\,2,\,3$ in red and $4,\,5,\,6$ in green is tossed. Let $A$ be the event, $'$ the number is even,$'$ and $B$ be the event, 'the number is red'. Are $A$ and $B$ independent?