$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.

$A$ bag contains $4$ white and $3$ red balls. Two draws of one ball each are made without replacement. Then the probability that both the balls are red is (in $/7$)

An urn contains $6$ blue, $4$ red, $3$ green, and $2$ yellow marbles. If four marbles are picked at random, what is the probability that at least one is red?

An anti-aircraft gun can take a maximum of $4$ 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. What is the probability that the gun hits the plane?

$A$ speaks truth in $60$ percent of cases and $B$ speaks truth in $70$ percent of cases. The probability that they will say the same thing while describing a single event is

Two coins are tossed. Find the probability that at least one head and one tail are obtained?