Probability of a boy to answer a question is 1/2 and a girl is 1/3 what is the probability that both of them answer correctly

There are two children in a family. What is the probability that both of them are boys?

The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability none of them will get the scholarship is

The probability that a boy will get a scholar ship is 0.90 and that a girl will get 0.80. What is the probability that at least one of them wil get the schloreship.

There are two childrens in a family. The probability that both of them are boys is

In a test a candidate may have answered a question in 3 ways. The question is a multiple choice question with 4 choices one of which is the correct answer. He might have guessed the answer for which the probability is 1/3. He might have copied the answer for which the probability is 1/6. He might have known the answer. If he copied the answer the probability that his answer is correct is 1/8. Find the probability that he knew the answer given that he correctly answerd it.

What is the value of x, if the probability of guessing the correct answer to a certain test question is x/12 and the probability of not guessing the correct answer to this question is 2/3 ?