Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p₁ be the probability that the maximum of chosen numbers is at least 81 and p₂ be the probability that the minimum of chosen numbers is at most 40.

The value of $${{125} \over 4}{p_2}$$ is ___________.

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is ............

Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14p is ..........

Let S be the sample space of all 3 $$ \times $$ 3 matrices with entries from the set {0, 1}. Let the events E₁ and E₂ be given by

E₁ = {A$$ \in $$S : det A = 0} and

E₂ = {A$$ \in $$S : sum of entries of A is 7}.

If a matrix is chosen at random from S, then the conditional probability P(E₁ | E₂) equals ...............