You are given Three very rare three sided 'Phoenix Coins' where each of the three sides are equally likely to reveal itself upon a toss. The 'Phoenix Coin' sides and associated values are as follows: Phoenix Head = 0 'Tears' Phoenix Tail = -3 'Tears' Phoenix Fire = 12 'Tears'. How many (A) Phoenix Coin combinations; and (B) outcomes of Phoenix 'Tears' are possible if you were to toss Ten (15) Phoenix Coins? What is the (C) Expected Value of Phoenix 'Tears' if you were to toss Fourty (40) Phoenix Coins?

r1

You are rolling two dice, one red and one green. Now suppose we only care about sum of the dice. What are the different outcomes and their frequencies?

a pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?

Two dice, a 8-sided one and a  10-sided one are shaken in a cup then "rolled" onto a table.  How many possible outcomes are there?

If we roll a 6-sided dice, what is the probability of rolling a number less than 3?  Leave your answer in simplest fraction form.

B. Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field goal attempt that an offensive player can take inside of the three-point line and is worth 2 points. To practice this, Piel has to choose four different shooting spots among the five different spots in where he is comfortable of shooting. In previous games, his shot selection is 5% from the right baseline (Spot 1), 15% from the right elbow (Spot 2), 20% from the top of the key (Spot 3), 25% from the left elbow (Spot 4) and 35% from the left baseline (Spot 5). In this drill, a shooting spot can be selected once, multiple times, or not at all. This drill illustrates a random experiment with distribution. To help Piel decide, below is the partial table for the means and standard deviations of the random variable, Y, or the number of times he shoot the ball in a shooting spot. Shooting Spot E[Y] SD[Y] Spot 1 0.2 0.4359 Spot 2 0.6 0.7141 Spot 3 0.8 0.8000 Spot 4 the mean of 1.4 by will…

Two dice are rolled. Find the odds of roling the following (a) in reduced form, the odds in favor of rolling a sum of 5 areoU (Simplity your answers.) (a) A sum of 5 (b) A sum of 9 or 11 (c) A Sum less than 5 (d) Not a sum of 8 (b) in reduced form, the odds in favor of rolling a sum of 9 or 11 are (Simplity your answers) (e) In reduced form, the odds in favor of rolling a sum less than 5 are to (Simplity your answers.) (d) in reduced form, the odds in favor of not rolling a sum of 8 are (Simplity your answers.)