Why is tossing a coin considered to be a fair way of deciding which term should get the ball at the beginning of any game?

A man alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 on the die is

A bag contains n coins of which five of them are counterfeit with heads on both sides and the rest are fair coins. If one coin is selected from the bag and tossed, the probability of getting head is 5//8 then n=

A,B,C are tossing a coin on the condition that , the person who gets a Head first, wins the game. If A starts the game, then the probabilities of A, B and C to win the game are

If 4 fair coins are tossed find the probability of getting 2 heads and 2 talls.

If getting a head on a coin when it is tossed is considered as success, then the probability of having more number of failures when ten fair coins are tossed simultaneously, is

A fair coin is tossed a fixed number of times. If the probability of getting five heads is equal to that of getting seven heads, then the probability of getting four heads is

A fair coin is tossed a fixed number times . If the probability of getting seven heads is equal to that of getting nine heads then the probability of getting two heads is

A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 1/2, while it is 2/3 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. What is the probability that the coin drawn is fair ?