Consider the ways that a couple can have three children. Define the following events: Event M:...

Consider the ways that a couple can have three children. Define the following events:

Event M: They have a child of each gender.

Event N: They have at most one boy.

Suppose that they are more likely to have a boy (B) than a girl (G), by a ratio of 11 to 9.

a. Using set notation like I did in the 2-child case (due to time, I didn’t use set notation in the 3-child case), list out the events M, N, and M ∩ N.

b. Carefully calculate the exact values of P(M), P(N), and P(M ∩ N), writing each probability to 4, 5, and 6 decimal places, respectively.

c. Use the definition of independent events to determine if M and N are independent.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

a couple intends to have three children. assume (for some reason) that having a boy or...

a couple intends to have three children. assume (for some reason) that having a boy or a girl are not equally likely events, and that p(boy)=.4 and p(girl)=.6 for each delivery also assume the births are independent of each other (a. what is the sample space of this experiment? Use a tree diagram and label the branches with their corresponding probabilities. Then make a table including all outcomes from the experiment with their associated probabilities. (b. Find the probability that...

55. A family has three children. Let A be the event that they have less than...

55. A family has three children. Let A be the event that they have less than two girls and B be the event that they have exactly two girls. (a) List all of the basic outcomes in A. (b) List all of the basic outcomes in B. (c) List all of the basic outcomes in A ∩ B (d) List all of the basic outcomes in A U B. (e) If male and female births are equally likely, what is...

Consider a family with a mother, father, and two children. Consider the following set of events:...

Consider a family with a mother, father, and two children. Consider the following set of events: A1 = {mother has influenza} A2 = {father has influenza} A3 = {first child has influenza} A4 = {second child has influenza} B = {at least one child has influenza} C = {at least one parent has influenza} D = {at least one family member has influenza} 1. What does A1 ∪ A2 mean? Which answer is correct? Please provide explanation a. Both the...

For the following exercises, assume that there are n ways an event A can happen...Use the Multiplication Principle of counting to explain how many ways event A and B can occur.

For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A and B are non-overlapping.Use the Multiplication Principle of counting to explain how many ways event A and B can occur.

A couple plans to have children until they get a girl, but they agree they will...

A couple plans to have children until they get a girl, but they agree they will not have more than three children, even if all are boys. Assume that the probability of having a girl is 52.00 %. a) Create a probability model for the number of children they'll have. b) Find the expected number of children. c) Find the expected number of boys they'll have.

The three children of a farm couple are sent to the market to sell 90 apples.

Use ILPThe three children of a farm couple are sent to the market to sell 90 apples. Karen, the oldest, carries 50 apples; Bill, the middle one, carries 30; and John, the youngest carries only 10. The parents have stipulated 5 rules: (1) The selling price is either $1 for 3 apples or $2 for 1 apple. (2) Each child may exercise one or both options of the selling price. (3) Each of the three children must return with exactly...

To the right are the outcomes that are possible when a couple has three children. Assume...

To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly 1 girl. 1st 2nd 3rd boy boy boy boy boy girl boy girl boy boy girl girl girl boy boy girl boy girl girl girl boy girl girl girl

There is a married couple with three children and an annual income of $24,000 who, because...

There is a married couple with three children and an annual income of $24,000 who, because of the standard deduction and personal exemptions, owe no federal income tax. Suppose the child tax credit is such that for families that pay less income tax than the child credit to which they are entitled the law allows them to receive a refund of 15% of earnings over $12,000, up to a maximum of $800. a. What is the family’s tax credit per...

Consider a couple who jointly earn $100,000, have two children, pay $6,000 in child care expenses...

Consider a couple who jointly earn $100,000, have two children, pay $6,000 in child care expenses for one child, pay $20,000 in college tuition for the other child (who qualifies as a dependent), pay $6,000 in mortgage interest, and pay $9,600 in medical expenses. It makes sense to use a spreadsheet to do this problem. Assume they file their tax return jointly. ? Tuition expenses are an allowable adjustment to income ? Personal exemptions are $3,000 per person ? The...

6. Consider a couple who jointly earn $100,000, have two children, pay $6,000 in child care...

6. Consider a couple who jointly earn $100,000, have two children, pay $6,000 in child care expenses for one child, pay $20,000 in college tuition for the other child (who qualifies as a dependent), pay $6,000 in mortgage interest, and pay $9,600 in medical expenses. It makes sense to use a spreadsheet to do this problem. Assume they file their tax return jointly. .? Tuition expenses are an allowable adjustment to income .? Personal exemptions are $3,000 per person .?...

Subjects