A biased coin with probability `P,(0 < p ,1)` of heads is tossed unitl a head appear for the first time. If the probability that the number of tosses required is even is `2/5` then `p=`

A biased coin with probability of head as 2/3 is tosses 4 times. If it is known that both head and tail occur, then probability that head and tail occur alternately is

A purse contains 3 coins C_(1), C_(2), C_(3) . Where C_(1) is a fair coin, C_(2) is a biased coin with probability (2)/(3) of showing up head and C_(3) is a fake coin containing head on both sides. One of the coins is selected at random and tossed twice. If head is obtained on both the tosses, then the probability that the coin selected is not a fair coin is p. Then p =

A biased coin in which probability of getting head is twice to that of tail. If coin is tossed 3 times then the probability of getting two tails and one head is

A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of 'p is :

A biased coin has (2)/(3) probability of landing heads.If the coin is flipped 50 xx,then the probability that the total number of heads is even is:

A coin is biased so that the probability of falling head when tossed is (1)/(4) . If the coin is tossed 5 times , the probability of obtaining 2 heads and 3 tails is

There are two coins, one unbiased with probability 1/2 of getting heads and the other one is biased with probability 3/4 of gatting heads. A coin is selected at random and tossed.It shows heads up. Then the probability that the unbiased coin was selected is-

There are two coins, one unbiased with probability 1/2 or getting heads and the other one is biased with probability 3/4 of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is