Solve math

1. Two dice are rolled. a) Define the sample space for this probability experiment. How many outcomes are there? What are the possible outcomes? b) Find the probability of each of the following outcomes: i) Snake Eyes (2 one's) ii) A sum greater than 4 iii) An even sum iv) At least one die is a 3 v) An odd sum or a sum of 8 2. A dice is rolled. A card is drawn from a deck of face cards (i.e. only Jack, Queen, King of each suit). A coin is flipped. a) Draw a tree diagram to define the sample space for this game. b) You win the game if you toss tails, draw a heart, and roll an even number. Find the probability that you do not win. 3. A six-member committee is formed to plan a Christmas formal. The members of the group are to be selected from five teachers and nine students. If the members are randomly selected, what is the probability that it will include at least two teachers? 4. Matt and his wife have 20 good friends, twelve of them are male and eight of them are female. They decide to have a diner party but can invite only eight guests. They decide to invite their guests by drawing their names from a hat. What is the probability that a) There will be an equal number of males and females at the dinner party? b) Mandie will be among those invited? c) There will be only one female guest? d) They will have only male guests? e There will be at least one female quest