Three coins are tossed once. Find the probability of getting $3$ tails.

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd,the coin is tossed twice. Write the sample space for this experiment.

If $X_1, X_2, \ldots, X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$ for $r = 1, 2, \ldots, n$,then the probability that none of the $n$ events occur is

$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.

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