Probability

The probability that a randomly chosen 5 - digit number is made from exactly two digits is:

A die is thrown two times and the sum of the scorers appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared at least once is

Let the focal chord PQ of the parabola y² = 4x make an angle of 60° with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, a), then 5a² is equal to:

Let E? denote the complement of an event E. Let E?, E?, and E? be any pairwise independent events with P(E?)>0 and P(E?∩E?∩E?)=0. Then P(E?∩E?/E?) is equal to

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is:

Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD=8m, BC=11m and AB=10m; then the distance (in meters) of a point M on AB from the point A such that MD²+MC² is minimum is [numerical value].