Three students `Aa n dBa n dC` are in a swimming race. `Aa n dB` have the same probability of winning and each is twice as likely to win as `Cdot` Find the probability that the `BorC` wins. Assume no two reach the winning point simultaneously.

Three persons A,B,C take part in a competition.A is 4 times as likely as B to win,and B is thrice as likely as C to win .Find the probability of A,B,C to win the competition.

Aa n dB participate in a tournament of best of 7 games. It is equally likely that either A wins or B wins or the game ends in a draw. What is the probability that A wins the tournament.

Three candidates X, Y, and Z are going to play in a chess competition to win FIDE (World Chess Federation) cup this year. X is thrice as likely to win as Y and Y is twice as likely as to win Z. Find the respective probability of X, Y and Z to win the cup

Aa n dB are two independent events. The probability that both Aa n dB occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of the occurrence of Adot

Whenever horses a , b , c race together, their respective probabilities of winning the race are 0.3, 0.5, and 0.2 respectively. If they race three times, the probability that the same horse wins all the three races, and the probability that a , b ,c each wins one race are, respectively. a. 8//50 ,9//50 b. 16//100 ,3//100 c. 12//50 , 15//50 d. 10//50 ,8//50

An unbiased die is such that probability of number n appearing is proportional to n^2(n=1,2,3,4,5,6)dot The die is rolled twice, giving the numbers aa n db . Then find the probability that a< b

Two number aa n db aer chosen at random from the set of first 30 natural numbers. Find the probability that a^2-b^2 is divisible by 3.

Two boys A and B find the jumble of n ropes lying on the floor. Each takes hold of one loose end randomly. If the probability that they are both holding the same rope is 1/(101) then the number of ropes is equal to

Aa n dB play a series of games which cannot be drawn and p , q are their respective chance of winning a single game. What is the chance that A wins m games before B wins n games?