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 :-

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.

$A$ die marked $1, 2, 3$ in red and $4, 5, 6$ in green is tossed. Let $A$ be the event 'the number is even' and $B$ be the event 'the number is red'. Are $A$ and $B$ independent?

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 be a diamond.

$A$ bag contains $3$ red and $3$ white balls. If two balls are drawn one after another,what is the probability that they are of different colors?

$4$-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