$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

Two players play the following game: $A$ writes $3, 5, 6$ on three different cards; $B$ writes $8, 9, 10$ on three different cards. Both draw randomly two cards from their collections. Then,$A$ computes the product of the two numbers he/she has drawn,and $B$ computes the sum of the two numbers he/she has drawn. The player getting the larger number wins. What is the probability that $A$ wins?

The probability of hitting a target by three marksmen is $\frac{1}{2}, \frac{1}{3},$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu,$ then $\lambda + \mu$ is equal to :-

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

Three coins are tossed. Describe three events which are mutually exclusive but not exhaustive.

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 black card.