HELP 2 PROBABILITY1. A dog owner has 2 beagles, 2 golden retrievers and one cocker spaniel. If two of these dogs are randomly selected, determine the following:a. List the sample space of this experimentb. What is the probability of selecting 2 dogs of the same type?2. An experiment consists of tossing two ordinary dice and adding the two numbers. Determine the probability of obtaining:a. A sum of 8 b. A sum less than or equal to 4 c. A sum greater than 73. Draw a probability tree for the following experiment:Choosing an M&M from a bowl containing one each of an orange, red, blue, yellow, brown and green M&M and then having either a Coke or a Pepsi.4. If an experiment consists of spinning Spinner A and then spinning Spinner B, Red Blue Pink Red Purplea. What is the probability of spinning blue then red? Red Pinkb. What is the probability of spinning purple then pink? Spinner A Spinner B5. 12 regular playing cards having 5 hearts, 4 clubs, and 3 diamonds are shuffled and placed face down on the table. Determine the probability of selecting 2 clubs if:a. The first card selected IS returned to the table for the second selection. (An independentb. The first card selected is NOT returned to the table for the second selection. (Adependent event)6. A young child is given 9 uncolored geometric wooden pieces of approximately the same size: 3 triangular shaped, 3 square shaped, and 3 hexagonal shaped. The pieces are mixed up in a box and the child selects 3 hexagonal shaped pieces without replacement. The parent wonders if the child can distinguish between the hexagonal pieces and the other pieces, of if this was accidental.a. If such a selection is done randomly (selected one at a time), what is the probability to the nearest tenth of a percent of obtaining 3 hexagonal shapes from the 9 pieces?b. Does the evidence suggest that the child can distinguish the hexagonal shape from the 9 pieces?7. If a person is randomly selected from the U.S. population, the odds the person lives in California are 1 to 8.a. What is the probability of a randomly chosen person being from California?b. What are the odds of a randomly chosen person not being from California?8. A certain sweepstake ticket has four categories of prizes with the following probabilities of being PRIZE VALUE PROBABILITY $100,000 1/500,000 $ 50,000 1/250,000 $ 20,000 1/200,000 $ 10,000 1/100,000a. What is the expected value of buying these sweepstakes tickets?b. If each ticket is $1, is this a fair contest? (Why/why not?)
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