The probability that $A$ speaks truth is $4/5$,while the probability that $B$ speaks truth is $3/4$. The probability that $A$ and $B$ contradict each other when asked to reveal the fact is

Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is $\frac{1}{4}$ and the probability that the second student gets qualified in the same exam is $\frac{2}{5}$,then the probability that at least one of them gets qualified in that exam is

Three groups of children $A$, $B$, and $C$ contain boys and girls as given below. Group $A$ contains $3$ girls and $1$ boy, group $B$ contains $2$ girls and $2$ boys, and group $C$ contains $3$ boys and $1$ girl. If $1$ child is selected at random from each group, what is the probability that the three children selected consist of $1$ girl and $2$ boys?

Suppose $A$ and $B$ are two events such that $P(A) = 0.9$,$P(B) = 0.8$,and $P(A \cap B) \geq 0.7$. Then,we can conclude that such a case is . . . . . .

Two dice are thrown three times. What is the probability that the first throw shows $10$,the second throw shows $11$,and the third throw shows $12$?

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will be a diamond but not an ace.