Answer the following questions and show all work (including diagrams) to create a complete answer.
- A bag contains 3 red balls and 4 blue balls. Thomas reaches in the bag and picks a ball out at random from the bag. He places it back into the bag. Thomas then reaches in the bag and picks another ball at random.
- Draw a tree diagram to represent this problem.
- What is the probability that Thomas picks:
- 2 red balls
- a red ball in his second draw
- A teacher has a prize box on her front desk for when students do exceptional work in math class. Inside the box there are 20 math pencils and 10 very cool erasers. Janet completed a challenge problem for Ms. Cameron, and Ms. Cameron rewarded Janet’s innovative problem-solving approach with a trip to the prize box. Janet reaches into the box and picks out a prize and then drops it back in. Then she reaches in again and picks out a prize a second time.
- Draw a tree diagram to represent this problem.
- What is the probability that Janet reaches into the box and picks out an eraser on the second pick?
- Determine whether the following situations would require calculating a permutation or a combination:
- Selecting 3 students to attend a conference in Washington, D.C.
- Selecting a lead and an understudy for a school play
- Assigning students to their seats on the first day of school
- Solve for 7P5.
- Evaluate 4P2×5P3.
- How many different 4-digit numerals can be made from the digits of 56987 if a digit can appear just once in a numeral?
- In how many ways can the letters of the word REFERENCE be arranged?
- In how many ways can the letters of the word MISSISSIPPI be arranged?
- In how many ways can the letters of the word MATHEMATICS be arranged?
- If there are 4 chocolate chip, 2 oatmeal, and 2 double chocolate cookies in a box, in how many different orders is it possible to eat all of these cookies?
- A math test is made up of 15 multiple choice questions. 5 questions have the answer A, 4 have the answer B, 3 have the answer C, 2 have the answer D, and 1 has the answer E. How many answer sheets are possible?
- In how many ways can you select 17 songs from a mix CD of a possible 38 songs?
- If an ice cream dessert can have 2 toppings, and there are 9 available, how many different selections can you make?
- If there are 17 randomly placed dots on a circle, how many lines can be formed using any 2 dots?
- A committee of 4 is to be formed from a group of 13 people. How many different committees can be formed?
- There are 4 kinds of meat and 10 veggies available to make wraps at the school cafeteria. How many possible wraps have 1 kind of meat and 3 veggies?
- There are 15 freshmen and 30 seniors in the Senior Math Club. The club is to send 4 representatives to the State Math Championships.
- How many different ways are there to select a group of 4 students to attend the State Math Championships?
- If the members of the club decide to send 2 freshmen and 2 seniors, how many different groupings are possible?
- Students in BDF High School were asked about their preference regarding the new school colors. They were given a choice between green and blue as the primary color and red and yellow as the secondary color. The results of the survey are shown in the tree diagram below. You can see that 75% of the students choose green as the primary color. Of this 75%, 45% chose yellow as the secondary color. What is the probability that a student in BDF High School selected red as the secondary color if he or she chose blue as the primary color?
- 2 fair dice are rolled. What is the probability that the sum is even given that the first die that is rolled is a 2?
- 2 fair dice are rolled. What is the probability that the sum is even given that the first die rolled is a 5?
- 2 fair dice are rolled. What is the probability that the sum is odd given that the first die rolled is a 5?
- Steve and Scott are playing a game of cards with a standard deck of playing cards. Steve deals Scott a black king. What is the probability that Scott’s second card will be a red card?
- Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen’s second card will be a black card?
- Donna discusses with her parents the idea that she should get an allowance. She says that in her class, 55% of her classmates receive an allowance for doing chores, and 25% get an allowance for doing chores and are good to their parents. Her mom asks Donna what the probability is that a classmate will be good to his or her parents given that he or she receives an allowance for doing chores. What should Donna's answer be?
- At a local high school, the probability that a student speaks English and French is 15%. The probability that a student speaks French is 45%. What is the probability that a student speaks English, given that the student speaks French?
- At a local high school, the probability that a student takes statistics and art is 10%. The probability that a student takes art is 65%. What is the probability that a student takes statistics, given that the student takes art?
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