problem 1: A die is thrown as long as essential for an ace or 6 to turn up. Given that no ace turned up at the first two throws, determine the probability that at least three throws will be essential?

problem 2: Given that a student studied, the probability of passing a certain quiz is 0.99. Given that they didn’t study. The probability of passing the quiz is o.05 supposed that the probability of studying is 0.7. A student flunks the quiz. Determine the probability the he or she didn’t study?

problem 3: Considering the statistical properties of electron emission in a thermonic vacuum tube, determine the probability of no electron beam emitted in t seconds.

problem 4: Train X arrives at the station at random in the time interval (O, T) stopping for ‘a’ mins. Train Y arrives independently in the similar interval stopping for ‘b’ minutes

a) Determine the probability P which X will arrive before Y.
b) Determine the probability P2 which the trains will meet.
c) Supposing that they met, determine that probabilityP3 which X arrived before Y.

problem 5: The population of Cyprus is 75% Greek and 25% Turkish. 20% of the Greeks and 10% of the Turks Speak English. A visitor to the town meets someone who speaks English. Determine the probability that he is a Greek? Deduce your answer in terms of the population of the town.

problem 6: In a college entrance exam each candidate is admitted or rejected according to whether he has passed or failed the test. Of the candidates who are really capable, 80% passed the test and of the incapable, 25% passed the test. Given the 40% of the candidates are really capable, determine the proportion of the capable college students.

problem 7: Three players P1, P2 and P3 throw a die in that order and by the rules of game, the first one to obtain san ace will be the winner. Determine their Probabilities of winning.

problem 8: 10 percent of a certain population suffers from a serious disease. Person suspected of the disease is given two independent tests. Each test makes a right diagnosis 90% of time. Determine the probability that the person really ahs the illness given that the both tests are positive.

problem 9: A has one share in a lottery in which there are on prize and two blanks has three shares in a lottery in which there are three blanks and 6 blanks. Compare the probability of A’s successes to that of the B’s success.

problem 10: A and B throw alternatively with a pair of dice. A wins if he throws 6 Before B throws 7 and B if he throws 7 before A throws 7. If a starts show that the chance of winning is 30/61.