Four persons $A$, $B$, $C$ and $D$ throw an unbiased die, turn by turn, in succession till one gets an even number and wins the game. What is the probability that $A$ wins if $A$ begins?

The probabilities that players $A$ and $B$ of a team are selected for the captaincy for a tournament are $0.6$ and $0.4$, respectively. If $A$ is selected as the captain, the probability that the team wins the tournament is $0.8$ and if $B$ is selected as the captain, the probability that the team wins the tournament is $0.7$. Then the probability, that the team wins the tournament, is:

There are $2$ shelves. One shelf has $5$ Physics and $3$ Biology books,and the other has $4$ Physics and $2$ Biology books. What is the probability of drawing a Physics book?

$A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he throws $6$ before $B$ throws $7$,and $B$ wins if he throws $7$ before $A$ throws $6$. If $A$ begins,the probability of $A$ winning is:

Two dice are thrown and two coins are tossed simultaneously. The probability of getting prime numbers on both the dice along with a head and a tail on the two coins is

Two decks of playing cards are well shuffled and $26$ cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is