# (Answered) MATH399N Week 3 Assignment:Multiplication Rules for Probability and the Fundamental Counting Principle

Question

Given that P(A AND B)=0.70 and P(A|B)=0.94, what is P(B)?

# Question

The probability that a child watches cartoons after school is 0.56. The probability that the child requests a certain toy of a cartoon character given that the child watches cartoons after school is 0.89. What is the probability that a child will request a toy and watch cartoons after school?

Give your answer as a percent, rounded to two decimal places if necessary.

Question

Two friends are both pregnant, and find out they are each expecting twins!

• Let Abe the event that one friend is pregnant with identical twins, and note that P(A)=0.0045.
• Let Bbe the event that the other friend is pregnant with fraternal twins, and note that P(B)=0.01.

A and B are independent events. What is the probability that one friend is pregnant with identical twins, and one friend is pregnant with fraternal twins?

Give your answer as a percent, rounded to four decimal places if necessary.

# Question

A couple has two children. Let A be the event that their first child is a boy, and note that P(A)=51.2%. Let B be the event that their second child is a girl, with P(B)=48.8%.

A and B are independent events. What is the probability that the couple has a first child that is a boy and a second child that is a girl?

# Question

The probability that a car has a certain factory defect is 825. The probability that a car has a certain factory defect and needs an oil change is 750. What is the probability that a car needs an oil change given that it has a certain factory defect?

# Question

If you roll a fair die and then roll a second fair die, what is the probability that you roll a 1, 2, or 3 on the first die and roll a 5 on the second die?

# Question

Given that P(A AND B)=0.29 and P(A|B)=0.67, what is P(B)?

# Question

The probability that a student will take loans to pay for their undergraduate education is 0.85, and the probability that a student will go to graduate school given that the student took loans to pay for their undergraduate education is 0.13. What is the probability that a student will go to graduate school and take loans to pay for their undergraduate education?

# Question

If A and B are independent events with P(A)=0.90 and P(A AND B)=0.54, find P(B).

# Solution

Question

Given that P(A AND B)=0.70 and P(A|B)=0.94, what is P(B)?