A fair die is tossed repeatedly. `A` wins if if is 1 or 2 on two consecutive tosses and `B` wins if it is 3,4,5 or 6 on two consecutive tosses. The probability that `A` wins if the die is tossed indefinitely is a.`1//3` b. `5//21` c. `1//4` d. `2//5`

An unbiased coin is tossed 6 times. The probability that third head appears on the sixth trial is a. 5//16 b. 5//32 c. 5//8 d. 5//64

A fair coin is tossed 10 times. Then the probability that two heads do not occur consecutively is a. 7//64 b. 1//8 c. 9//16 d. 9//64

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses required. The probability that X=3 equals

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The probability that X=ge3 equals

A fair coin is tossed 100 times. The probability of getting tails 1, 3, .., 49 times is 1//2 b. 1//4 c. 1//8 d. 1//16

Aa n dB play a game of tennis. The situation of the game is as follows: if one scores two consecutive points after a deuce, he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is 2/3. The game is a deuce and A is serving. Probability that A will win the match is (serves are change after each game) a. 3//5 b. 2//5 c. 1//2 d. 4//5

A four figure number is formed of the figures 1, 2, 3, 5 with no repetitions. The probability that the number is divisible by 5 is a. 3//4 b. 1//4 c. 1//8 d. none of these

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The conditional probability that Xge6 given Xgt3 equals

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 in the dice is a. 3//4 b. 1//2 c. 1//3 d. none of these

In a game a coin is tossed 2n+m times and a player wins if he does not get any two consecutive outcomes same for at least 2n times in a row. The probability that player wins the game is a. (m+2)/(2^(2n)+1) b. (2n+2)/(2^(2n)) c. (2n+2)/(2^(2n+1)) d. (m+2)/(2^(2n))