If three students $A, B, C$ independently solve a problem with probabilities $\frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively,then the probability that the problem will be solved is

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:

One card is drawn at random from a pack of $52$ playing cards. The probability that it is an ace,a black king,or the queen of hearts is:

$A$ card is drawn at random from a pack of $52$ cards. The probability that the drawn card is a court card,i.e.,a jack,a queen,or a king,is:

If $A, B$ and $C$ are three events of a random experiment with $P(A)=0.4, P(B)=0.3$ and $P(A \cap B)=0.2$,then the probability that neither $A$ nor $B$ occurs is

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$. Then the probability of the problem being solved is