An anti-aircraft gun takes four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first,second,third,and fourth shots are $0.4, 0.3, 0.2$,and $0.1$ respectively. The probability that the gun hits the plane is:

Three coins are tossed simultaneously. Consider the events $E$: 'three heads or three tails',$F$: 'at least two heads',and $G$: 'at most two heads'. Of the pairs $(E, F)$,$(E, G)$,and $(F, G)$,which are independent and which are dependent?

In a single throw of two dice,the probability of getting a sum of more than $7$ is

If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is

$A$ 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 $p(w_3)$.

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S = \{x \in \mathbb{Z} : x(66 - x) \geq \frac{5}{9} M\}$ and the event $A = \{x \in S : x \text{ is a multiple of } 3\}$. Then $P(A)$ is equal to