Consider an unbiased cubic die with opposite faces coloured identically and each face coloured red, blue or green such that each color appears only two times on the die. If the die is thrown thrice, the probability of obtaining red colour on top face of the die at least twice is ________.

A box contains $$25$$ parts of which $$10$$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

The probability that a student knows the correct answer to a multiple choice question is $${2 \over 3}$$. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $${1 \over 4}$$. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is

A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is