When two dice are thrown, the probability of getting an ordered pair $(x, y)$ such that $x^2+y^2 \leq 25$, where $x$ and $y$ are the numbers that show up on the two dice, is:

Describe the sample space for the indicated experiment: $A$ coin is tossed and then a die is rolled only in case a head is shown on the coin.

Three students $X, Y$ and $Z$ appear for an examination. The probability of $X$ passing the examination is $\frac{1}{5}$,the probability of $Y$ passing the examination is $\frac{1}{4}$ and the probability of $Z$ failing the examination is $\frac{2}{3}$. The probability that at least two of them pass the exam is

$A$ single letter is selected at random from the word $PROBABILITY$. The probability that the selected letter is a vowel is

$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by $3$ is

Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined: $P(A) = 0.5$,$P(B) = 0.7$,$P(A \cap B) = 0.6$.