Two coins are tossed. Find the probability that at least one head and one tail are obtained?

$A$ basket contains $4$ red,$5$ blue,and $3$ green marbles. If three marbles are picked at random,what is the probability that either all are green or all are red?

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

The probability that a man will be alive $25$ years hence is $0.3$ and the probability that his wife will be alive $25$ years hence is $0.4$. Find the probability that $25$ years hence,both will be alive.

Two dice are thrown. If the first die shows $5$,then the probability that the sum of the numbers on both dice is $8$ or more than $8$ is:

$A$ man speaks truth in $80 \%$ of the cases and another in $90 \%$ of the cases. While stating the same fact,what is the probability that they contradict each other?