Let $A$, $B$, and $C$ be three events such that $P(A \cap \bar{B} \cap \bar{C}) = 0.6$, $P(A) = 0.8$, and $P(\bar{A} \cap B \cap C) = 0.1$. Then, the value of $P(\text{at least two among } A, B, \text{ and } C)$ equals:

$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

When a certain biased die is rolled,a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with probability $\frac{1}{6}+x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0 < x < \frac{1}{6}$,and the probability of obtaining a total sum of $7$ when such a die is rolled twice is $\frac{13}{96}$,then the value of $x$ is:

Out of the given $25$ consecutive positive integers, three integers are drawn. If the least integer among the given $25$ integers is an odd number, then the probability that the sum of the three integers drawn is an even number is

Three dice are thrown simultaneously. What is the probability of obtaining a total of $17$ or $18$?

Three coins are tossed once. Find the probability of getting at least $2$ heads.