Define the sample space. To get simpler expressions, you canprefer the set notations.
(a) (6 Points) What is the sample space of choosing a real numberfrom interval [0, 1] which is larger than 0.5. Specify theproperties of the sample space. Design two different randomvariables for this task.
(b) (6 Points) You play rock-paper-scissors with your friend. Theone with total three wins or two subsequent wins will be the winnerof the game. Give a probability tree of you being the winner. Statethe sample space by using probability tree diagram.
(You can use nested probability trees to make the representationeasier. For example, you can generate a tree only for win-losspossibilities (without any information about rock-paper-scissors),one another tree for Win, including all possible cases with rock-paper-scissors, similarly one another tree for Loss, againincluding all possible cases with rock-paper-scissors)
