A and B throw a die alternately till one of them gets a ‘6’ and wins the game. Find the respective probabilities of winning if A starts first. (CBSE 2003, 2005)

  Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3 and that of Monica’s selection is 4/5. Find the probability that only one of them will be selected.

  The probability of A solving a problem is 3/7 and that of B solving it is 1/3. What is the probability that (i) at least one of them will solve the problem? (ii) Only one of them will solve the problem?

  There are three coins. One is a two-tailed coin (having tail on both faces), another is a biased coin that comes up head 60% of the times and third is an unbiased coin. One of the three coins is chosen at random and tossed, and it shows tails. What is the probability that it was a two-tailed coin?

  A doctor is to visit a patient. From the past experience it is known that the probabilities of the doctor coming by train, bus, scooter or taxi are 1/10, 1/5, 3/10, and 2/5 respectively. The probabilities that he will be late are ¼,1/3, and 1/12 if he comes by train, bus or scooter respectively but by taxi he will not be late. When he arrives he is late. What is the probability that he came by bus?

  A bag contains 7 red, 4 white and 5 black balls. Two balls are drawn at random, and are found to be white. What is the probability that all balls are white?

  A die is thrown again and again until three sixed are obtained. Find the probability of obtaining the third six in the sixth throw of the dice. a) 525/23357 b) 625/23328 c)725/23329 d) 825/23328

  Bring out the fallacy, if any, in the statement: “The mean of a binomial distribution is 5 and its variance is 9”. a) 9/5 b) 5 c) Given statement is wrong d) None

  Determine the binomial distribution (or B.D.) whose mean is 9 and whose standard deviation is 3/2. a) (1/4+3/4)12 b) (3/4+1/4)11 c) (1/4+3/4)10 d) None

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