Each of $a$ and $b$ can take values $1$ or $2$ with equal probability. The probability that the equation $ax^{2} + bx + 1 = 0$ has real roots is equal to

In a competition,$A, B$,and $C$ are participating. The probability that $A$ wins is twice that of $B$,and the probability that $B$ wins is twice that of $C$. Then,the probability that $A$ loses is:

An experiment consists of recording the boy-girl composition of families with $2$ children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

When three fair dice are tossed simultaneously,find the probability that the integers on all three dice are the same.

$A$ student appears for tests $I$, $II$, and $III$. The student is successful if they pass in tests ($I$ and $II$) $OR$ ($I$ and $III$). The probabilities of the student passing in tests $I$, $II$, and $III$ are respectively $p$, $q$, and $1/2$. If the probability of the student being successful is $1/2$, then:

Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows $2$ is