Three numbers are selected at random from the set ${1, 2, 3, \dots, 8}$ without replacement. Given that the minimum of the selected numbers is $3$ and the maximum is $6$, what is the probability that the third number is $4$ or $5$?

$A$ and $B$ are independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$,then $P(B)$ is

If a year is selected at random from the $22^{nd}$ century,what is the probability that it contains $53$ Sundays (in $/28$)?

An ellipse is inscribed in a circle and a point is chosen at random inside the circle. If the probability that this point lies outside the ellipse is $\frac{2}{3}$,then the eccentricity of the ellipse is $\frac{a\sqrt{b}}{c}$,where $\gcd(a, c) = 1$ and $b$ is a square-free integer. Find the value of $a \cdot b \cdot c$.

If the probabilities of three independent events occurring are $p_1, p_2, p_3$,what is the probability that at least one of these events occurs?

In a random experiment,a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to