For a Binomial distribution, B(n,p), where p+q=1, the sum and product of mean and variance are 8 and 12 respectively, when the value of n is:

If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1 then

A pair of dice is thrown, then the probability of getting a sum of 7, is

If the difference between mean and variance of a Binomial distribution is 1 and the difference of their squares is 5, then the probability of success is

If a fair coin is tossed 10 times, then the probability of obtaining at least one head is :

Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$. If all the three students try to solve the problem independently, the probability that the problem is solved, is:

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is