Let x denote the sum of two distinct numbers selected randomly from the set of numbers {1, 2, 3, 4, 5}. Construct the probability distribution for the random variable x.

An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 1000 tickets contain a prize of $5 each, 75 tickets have a prize of $10 each, 4 tickets have a prize of $1000 each, and 1 ticket has a prize of $5000. Let x be the random variable that denotes the net amount a player wins by playing this lottery. Write the probability distribution of x. Enter the exact answers. Enter your answers for x in increasing order. P(x) i i i i i i i Determine the mean and standard deviation of x. Round your answers to two decimal places. On average, the players who play this game are expected to i per ticket with a standard deviation of $ i

A bag contains 10 Blue balls, 10 Red balls, and 9 Green balls. Two balls are going to be drawn from the bag (one at a time) and then put to the side (they are not returned to the bag). Let event B blue ball chosen, R = Red ball chosen, and G- Green ball chosen. What is the probability they are both red? What is P(R and R)? Write an answer to 4 decimal places.

In a particular house, there are only 8 chairs. Whenever there is a party at this house some people have no where to sit. The number of people at these parties changes with each party. Call this number the random variable X. Past records indicate the probability distribution of X is as shown in the table below. Find the probability that everyone will have a place to sit at our next party. x 5 6| 7| 8| 10 > 10 9 P(X = x) 0.05 0.05 0.20 0.15 0.15 0.10 0.30 ..... O A. 0.55 O B. 0.15 O C. 0.05 O D. 0.45