Given two independent events $A$ and $B$ such $P(A)$ $=0.3,\, P(B)=0.6 .$ Find $P(A$ or $B)$

It is given that $P(A)=0.3, P(B)=0.6$

Also, $A$ and $B$ are independent events.

$P(A$ or $B)=P(A \cup B)$

$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$

$=0.3+0.6-0.18$

$=0.72$

Three coins are tossed simultaneously. Consider the event $E$ ' three heads or three tails', $\mathrm{F}$ 'at least two heads' and $\mathrm{G}$ ' at most two heads '. Of the pairs $(E,F)$, $(E,G)$ and $(F,G)$, which are independent? which are dependent ?

If $P\,({A_1} \cup {A_2}) = 1 - P(A_1^c)\,P(A_2^c)$ where $c$ stands for complement, then the events ${A_1}$ and ${A_2}$ are

The probability that a man will be alive in $20$ years is $\frac{3}{5}$ and the probability that his wife will be alive in $20$ years is $\frac{2}{3}$. Then the probability that at least one will be alive in $20$ years, is

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

If $A$ and $B$ are two events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{2}{3},$ then