statics and probability questions please help thanks :)

0.2 Tossing a biased coin n times independently. For each toss, the probability of getting heads is 133. Dene A be the event that the coin lands on heads exactly k times, it E n. (a). (6') Given the following scenarios: (i). k = 1, :2 unknown. (ii). k = 5, H unknown. (iii). 1: unknown, n = 12. For each scenario, which random variable can be used to describe the process of tossing and the possible outcome (1.9., the unknown)? (b). Let 1: =12 and k= 5, (i). (3') What is the probability that ev-t A occurs? (ii). (8') What is the probability that event A occurs if it is known that at least three heads appear? (iii). (3') Let B the event that the 1st or 2'"1 toss is heads. Are the events A and B independent? Explain it. No marks will be given without justification. (c). (5') Let X be the random variable indicating the number of tosses needed for obtaining k heads. Given 3: = 12 and k = 5, what is the expected value and variance ofX