probability of two spinners divided in 4 sections probability of government employees question joint probability

1. The first spinner is divided into 4 equal sections, and the second is divided into 3 equal sections. When these 2 fair spinners are each spun once, what is the probability that the product of the 2 numbers to which arrows point is even? Show all work and express your answer as a common fraction. (graph in the Document file)

2.A survey of 500 hundred government employees revealed that 329 were married, 186 were home owners and 295 had children and every employee surveyed said yes to at least one of these three questions.The survey also found that 83 were married and home owners, 217 were married and had children and 63 were home owners and had children.

a.How many of the government employees surveyed were married, home owners and had children?

b. How many of the government employees surveyed were married but did not have children?

c. Given an employee was a home owner and/or had children, what is the probability that the employee is also married? Hint – Show all work to get partial/full credit and try using a Venn diagram.

3. Using the following joint probability distribution. (Table in Document file )

a. Give the marginal distributions for Y and X.

b. Are X and Y independent?Show reasoning.

c. Give E(X), E(Y), Var(X) and Var(Y).

d. Give the covariance and correlation of X and Y.

e. Given Y = -2, what is the expected value and variance of X?