please also share explanations for each below

7. [10 Points] Conditional Probabilities. This is a simple exercise testing your understanding of the definitions. For each of the following questions carefully define (1) the sample space and (2) the event under consideration. Then (3) determine the probability. For full credit, you will have to display these three parts. We are given five cards. Three of the cards are black and they are numbered 1, 2, 3. The other two cards are red and they are numbered 1, 2. We pick two cards at random. (a) What is the probability that both cards are red? (b) What is the probability that both cards are red, if we know that at least one of them is red? (c) What is the probability that both cards are red, if we know that one of them is red card number 1