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

An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $$X'$$ s shock absorbers, $$96$$% are reliable. Of $$Y'$$ s shock absorbers, $$72$$% are reliable. The probability that a randomly choosen shock absorber, which is found to reliable, is made by $$Y$$ 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

An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at least one head is _______.