Problem Solving s5

The probability of a problem being solved by 3 students independently are (1)/(2), (1)/(3) and alpha respectively. If the probability that the problem is solved in P(S), then P(S) lies in the interval (where, alpha in (0, 1) )

The probabilites of A , B and C of solving a problem are (1)/(6),(1)/(5) " and " (1)/(3) respectively , What is the probability that the problem is solved ?

A computer solved several problems in succession. The time it took the computer to solve each succession problem was the same number of times smaller than the time it took to solve the preceding problem. How many problems were suggested to the computer if it spent 63.5 min to solve all the problems except for the first 127 min to solve all the problems except for the last one, and 31.5 min to solve all the problems except for the first two?

The probability of solving a specific problem independently by A and B are (1)/(3) and (1)/(5) respectively. If both try to solve the problem independently, find the probability that the problem is solved.

The odds against A solving the problem are 4 to 3 and the odds in favour of B solving the . problem are 7 to 5. Find the probability that the problem will be solved.

A and B try to solve the problem independently. The probability that A solves the problem is (1)/(2) and that B solves the problem is (1)/(3) . Find the probability that : (a) Both of them solve the problem (b) The problem is solved.

The probability that A can solve a problem is 4/5 and B can solve it is 2/3 .If both attempt the problem what is the probability that exactly one of the problem gets solved ?

For an initial screening of an admission test,a candidate is given fifty problems to solve.If the probability that the candidate can solve and problem is (4)/(5), then the probability that he is unable to solve less than two problems is: