Hi please use the given information to answer each part of the problem and please include a short explanation, drawing, or steps/formulas to improve my understanding of the problem. Please let me know if there's any questions, thank you!

Two coins are simultaneously tossed until one of them comes up a head and the other a tail. Assume the rst coin has bias p1 and the second has bias p2 and that the outcomes of all tosses are independent of each other, i.e., the outcomes of the two coins in each toss and among different tosses are independent. (3) What is the sample space for this random experiment? (b) Let X be the number of coin-pair tosses. What is the pmf of X? (c) What is the mean and variance of X