From a well-shuffled pack of cards,one card is drawn at random. The probability that the card drawn is an ace is

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

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

Two fair dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two events $A$ and $B$ are

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 not be a diamond.

$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.