1.) Determine whether the following distributions represent a probability distribution. Explain why to support your answer.2.) Your wallet contains two $1 bills, four $5 bills, six $10 bills and 8 $20 bills. a.) Construct a probability distribution for the data for randomly selecting one of the bills (assume that the bill will be replaced after each draw).b.) Calculate the mean, variance and standard deviation for the distribution. Please show your steps and use the equation editor to format your answers.c.) Use the range rule of thumb to determine if it would it be considered unusual to pull a $1 bill out of your wallet? Explain. 3.) In the New York State Lottery, you can bet $1 by selecting 4 numbers from 0 through 9 inclusive. You must select the same four numbers as the result from the lottery and they must be selected in the same order to win the $1000 prize. Please show your steps and use the equation editor to format your answers.a.) How many selections are possible?b.) What is the probability of winning the $1000 prize?c.) If you win, what is your net profit?d.) What is the expected value for winning the $1000 prize?4.) 5 patients qualify to have a surgical procedure performed. The doctor states that there is an 80% chance of a successful surgery. The random variable x represents a successful surgery. Find the following probabilities. Please set up your probabilities, show all steps for solving and use the equation editor to format your equations.a.) Probability of exactly 3 successful surgeries.b.) Probability of at least 3 successful surgeries.c.) Probability of more than 3 successful surgeries.d.) Probability of fewer than 3 successful surgeries.e.) Probability of no successful surgeries.f.) Probability of 5 successful surgeries.5.) 5 patients qualify to have a surgical procedure performed. The doctor states that there is an 80% chance of a successful surgery. Answer the questions below. Please show all steps for solving and use the equation editor to format your equations.a.) Calculate the mean, variance and standard deviation for the binomial probability distribution. Please show your steps and use the equation editor to format your answers.b.) Use the range rule of thumb to determine if it would it be considered unusual to have exactly 2 successful surgeries? Explain. c.) Based on your calculated statistics, if you needed to have the surgical procedure performed, would you choose this doctor? Explain.