1. From a box containing five quarters and two dimes, three coins are selected at random without replacement. Find the probability distribution for the total T of the three coins.

Given the cumulative distribution function (c.d.f) if x x. 0, x+4 F(x) = 6 1, Compute P(X = 1). ([Note] Since the given function F(x) is not continuous, you need to compute the left limit at x = 1.) a. 6 b. c. d. 2

A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X A. P(X = x) 2 0.227 6 10 0.015 11 15 20 .091 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)

In a large population, 68 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal (to at least 3 places) or fraction.

In a large population, 63 % of the people have been vaccinated. If 3 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?Give your answer as a decimal (to at least 3 places) or fraction

A committee of 4 is being formed randomly from the employees at a school: 6 administrators, 38 teachers, and 5 staff. What is the probability that all 4 members are administrators? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X P(X = x) 2 0.015 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)