A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :

Let E^C denote the complement of an event E. Let E₁ , E₂ and E₃ be any pairwise independent events with P(E₁) > 0

and P(E₁ $$ \cap $$ E₂ $$ \cap $$ E₃) = 0.

Then P($$E_2^C \cap E_3^C/{E_1}$$) 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 :

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :