If $E$ and $F$ are independent events such that $0 < P(E) < 1$ and $0 < P\,(F) < 1,$ then
$E$ and ${F^c}$ (the complement of the event $F$) are independent
${E^c}$ and ${F^c}$ are independent
$P\,\left( {\frac{E}{F}} \right) + P\,\left( {\frac{{{E^c}}}{{{F^c}}}} \right) = 1$
All of the above
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 spade'
$F:$ 'the card drawn is an ace'
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
Events $E$ and $F$ are such that $P ( $ not $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.
Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing $15$ oranges out of which $12$ are good and $3$ are bad ones will be approved for sale.