Probability - Numerical Problems, Solved and Explained

Probabilities of solving a specific problem in dependently by A and B are 1/2a n d1/3 respectively. If both try to solve the problem independently find the probability that : The problem is solved Exactly one of them solves the problem.

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) )

Given the probability that A can solve a problem is 2/3 and the probability that B can solve the same problem is 3/5. Find the probability that none of the two will be able to solve the problem.

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

Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that (i) the problem is solved (ii) exactly one of them solves the problem.

A problem in mathematics is given to three stdents A,B,C and their chances of solving the problem are 1/2 , 1/3 and 1/4 respectively . The probability that the problem is solved is

The probability of solving a problem by three students are 1/3,1/4,1/5 . Find the probability that the problem will be solved if all three students try the problem simultaneously.

The probabilities of A , B and C solving a problem independently are respectively (1)/(4) , (1)/(5) , (1)/(6) . If 21 such problems are given to A , B and C then the probability that at least 11 problems can be solved by them is

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

Four person independently solve a certain problem correctly with probabilities 1/2,3/4,1/4,1/8dot Then the probability that he problem is solve correctly by at least one of them is (235)/(256) b. (21)/(256) c. 3/(256) d. (253)/(256)