Probability
There are 7 students in a class: 2 boys and 5 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a girl?
A fair sixsided die is rolled. What is the probability that the result is a 4? Write your answer as a simplified fraction.
A game at the carnival offers these odds: you get to roll a tensided die, and if you roll a 4, you make 7 dollars. Unfortunately, if you roll anything else, you lose 6 dollars.
How much money do you expect to make (or lose) playing this game?
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time.
What is the probability of Tim Duncan making ALL of his next 5 free throw attempts?
A bag contains 3 red balls, 6 green balls, and 2 blue balls.
If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be green as well? Write your answer as a simplified fraction.
A baker has a whole baguette.
How many cuts must she make to have exactly 6 even slices?
Emily is 3 times as old as Christopher and is also 10 years older than Christopher.
How old is Christopher?
Emily rode her bike for 3 miles on each of the past 5 days.
How many miles did Emily ride her bike altogether?
Mary has 4 eggplants for every 3 kiwis. Write the ratio of eggplants to kiwis as a simplified fraction.
In Spanish class, the girl to boy ratio is 3 to 5.
If there are a total of 16 students, how many girls are there?
If Lisa can type 70 words per minute and it took her 21 minutes to type her latest essay, how many words did the essay have?
Jessica traveled by car at an average speed of 23 miles per hour.
Then, she traveled by train at an average speed of 65 miles per hour.
In total, she traveled 116 miles for 4 hours.
How many miles did Jessica travel by train? (Round to the nearest mile.)
It takes 34 minutes for 6 people to paint 6 walls.
How many minutes does it take 11 people to paint 11 walls?
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a girl?
A fair sixsided die is rolled. What is the probability that the result is a 4? Write your answer as a simplified fraction.
A game at the carnival offers these odds: you get to roll a tensided die, and if you roll a 4, you make 7 dollars. Unfortunately, if you roll anything else, you lose 6 dollars.
How much money do you expect to make (or lose) playing this game?
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time.
What is the probability of Tim Duncan making ALL of his next 5 free throw attempts?
A bag contains 3 red balls, 6 green balls, and 2 blue balls.
If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be green as well? Write your answer as a simplified fraction.
A baker has a whole baguette.
How many cuts must she make to have exactly 6 even slices?
Emily is 3 times as old as Christopher and is also 10 years older than Christopher.
How old is Christopher?
Emily rode her bike for 3 miles on each of the past 5 days.
How many miles did Emily ride her bike altogether?
Mary has 4 eggplants for every 3 kiwis. Write the ratio of eggplants to kiwis as a simplified fraction.
In Spanish class, the girl to boy ratio is 3 to 5.
If there are a total of 16 students, how many girls are there?
If Lisa can type 70 words per minute and it took her 21 minutes to type her latest essay, how many words did the essay have?
Jessica traveled by car at an average speed of 23 miles per hour.
Then, she traveled by train at an average speed of 65 miles per hour.
In total, she traveled 116 miles for 4 hours.
How many miles did Jessica travel by train? (Round to the nearest mile.)
It takes 34 minutes for 6 people to paint 6 walls.
How many minutes does it take 11 people to paint 11 walls?
Combinations
Yvonne is packing her bags for her vacation. She has 6 unique tigers, but only 3 fit in her bag.
How many different groups of 3 tigers can she take?
How many different groups of 3 tigers can she take?
Permutations
How many unique ways are there to arrange the letters in the word APE?
The Handshake
There are 6 people in a room.
If everyone shakes everyone else's hand exactly once, how many handshakes occurred?
If everyone shakes everyone else's hand exactly once, how many handshakes occurred?
How many seconds are there in a year?
Take a few moments to figure out how many seconds there are in a year. How many minutes are there in a year? How many hours?
Carlos burns 75 calories for every 15 minutes he walks
How many calories will Carlos burn if he walks for 45 minutes?
Carlos wants to burn 300 calories. How many minutes must Carlos walk in order to burn 300 calories?
Carlos wants to burn 300 calories. How many minutes must Carlos walk in order to burn 300 calories?
Where did the other dollar go?
Three people walk into a motel and ask for a room. The desk clerk says a room costs 60 dollars, so each person pays 20 dollars towards the cost.
Later, the clerk realizes he made a mistake, that the room should have only been 55 dollars.
He calls the bellboy over and asks him to refund the other 5 dollars to the 3 people.
The bellboy, not wanting to make a mess dividing the 5 dollars three ways, decides to lie about the price, refunding each person 1 dollar, keeping the other 2 dollars for himself.
Ultimately each person paid 19 dollars towards the room and the bellboy got 2 dollars, for a total of 59 dollars.
But the original charge was 60 dollars. Where did the other dollar go?
Later, the clerk realizes he made a mistake, that the room should have only been 55 dollars.
He calls the bellboy over and asks him to refund the other 5 dollars to the 3 people.
The bellboy, not wanting to make a mess dividing the 5 dollars three ways, decides to lie about the price, refunding each person 1 dollar, keeping the other 2 dollars for himself.
Ultimately each person paid 19 dollars towards the room and the bellboy got 2 dollars, for a total of 59 dollars.
But the original charge was 60 dollars. Where did the other dollar go?
Wednesday, September 19, 2012
Today's word problems of the day
1. Jenny had a whole pie. She cut it into 8 pieces. She ate one piece and gave Karen and Candy 2 pieces. What is the fraction of the pie that is left?
2. Mindy baked a dozen cookies. She ate 2. She gave Missy 2, Cindy 2, and Shelly 2. What is the fraction for the number of pieces that are left? 3. Tim had 12 baseball cards. He gave Steve 3 cards, Billy 3 cards, and Bob 3 cards. What is the fraction of cards that he gave away? 4. Julie had 35 blank computer disks that she wanted to share with her friends, Cindy and Jessie. She wanted to divide the disk among the three of them so that each one would have an equal amount. What is the fraction of disks that she would have left over? 5. Missy had a birthday party. She had a sheet cake that she could cut in 12 equal sizes. She wanted to invite 20 friends over for her birthday party. How many sheet cakes would she need if she friend received two pieces of cake? Would there be any cake left over? If so, what would the fraction be? 
6. Missy had 2 pitchers of fruit punch for her birthday party. She could fill 24 cups using 1 pitcher. Would she have enough fruit punch so that each of her 20 friends could have a refill? If so, would she have any left? What fraction would she have left?
7. Carol had a large bag of candy that contained 169 pieces. She wanted to divide the candy into equal amounts with her friends, Susan and Megan. What fraction of candy would she have left after dividing the candy? 8. Christy bought two bags of Christmas candy for $4.00. She gave the cashier $10.00. How much would she get back? What is the fraction of her money that she spent? 9. Beth had 96 pictures. She gave her two friends, Megan and Christy, 2/3 of her pictures, and she kept 1/3. How many pictures did Beth give away? 10. Bill had $135 that he collected from doing lawn work. His friends, Tom and Jim, helped with the lawn work, too. He needed to divide the amount equally. Would he have anything left over? If he did, what fraction would be left? 
The RaceXavier, Yolanda, and Zollie finished first, second and third in a race; but not necessarily in that order.
List all the possible orders that they could have finished. If Xavier was not first, how many possible orders of finish were there? How many numbers?A number cube or a dice has six surfaces or faces. Each side is marked with a different number of dots on each side. How many dots are there altogether?

I am thinking of a numberSam thought of a number between ten and twenty.
Then he gave a clue: You say the number when you count by twos and when you count by threes, but not when you count by fours. Of what number was Sam thinking? The Treasure MapTom studied the treasure map. He started at the tree and walked north five steps. He turned right and walked seven steps. He turned right again and walked nine steps. Then he turned left and walked three steps. Finally, he turned left and walked four steps and stopped. In which direction was he facing?
How many steps awe was the tree? 
Answers
1. Jenny had a whole pie. She cut it into 8 pieces. She ate one piece and gave Karen and Candy 2 pieces. What is the fraction of the pie that is left?
They had 5/8 left. They ate 3/8 of the pie.
2. Mindy baked a dozen cookies. She ate 2. She gave Missy 2, Cindy 2, and Shelly 2. What is the fraction for the number of pieces that are left?
They ate 8/24. They had 16/24 left
3. Tim had 12 baseball cards. He gave Steve 3 cards, Billy 3 cards, and Bob 3 cards. What is the fraction of cards that he gave away?
He gave away 9/12.
4. Julie had 35 blank computer disks that she wanted to share with her friends, Cindy and Jessie. She wanted to divide the disk among the three of them so that each one would have an equal amount. What is the fraction of disks that she would have left over?
She 2/35 left. Each of them would have 11 disks, which total 33. She would have 2 left.
5. Missy had a birthday party. She had a sheet cake that she could cut in 12 equal sizes. She wanted to invite 20 friends over for her birthday party. How many sheet cakes would she need if she friend received two pieces of cake? Would there be any cake left over? If so, what would the fraction be?
She would need four sheet cakes for her friends to have two pieces. She would have 8 pieces left. The fraction would be 8/48.
6. Missy had 2 pitchers of fruit punch for her birthday party. She could fill 24 cups using 1 pitcher. Would she have enough fruit punch so that each of her 20 friends could have a refill? If so, would she have any left? What fraction would she have left?
She could fill 48 cups. Each of her 20 friends could have a refill. She would have some left. She would have 8/48 left.
7. Carol had a large bag of candy that contained 169 pieces. She wanted to divide the candy into equal amounts with her friends, Susan and Megan. What fraction of candy would she have left after dividing the candy?
She could divide 169 by 3. She would have 1/169 left. Each one would get 15 pieces, and one left over.
8. Christy bought two bags of Christmas candy for $4.00. She gave the cashier $10.00. How much would she get back? What is the fraction of her money that she spent?
She would get back $6.00. She spent 4/10 of her money.
9. Beth had 96 pictures. She gave her two friends, Megan and Christy, 2/3 of her pictures, and she kept 1/3. How many pictures did Beth give away?
She gave away 2/3 of 96 = 64 pictures.
10. Bill had $135 that he collected from doing lawn work. His friends, Tom and Jim, helped with the lawn work, too. He needed to divide the amount equally. Would he have anything left over? If he did, what fraction is left?
He could divide $135 equally between the three of them. He would't have anything left over.
They had 5/8 left. They ate 3/8 of the pie.
2. Mindy baked a dozen cookies. She ate 2. She gave Missy 2, Cindy 2, and Shelly 2. What is the fraction for the number of pieces that are left?
They ate 8/24. They had 16/24 left
3. Tim had 12 baseball cards. He gave Steve 3 cards, Billy 3 cards, and Bob 3 cards. What is the fraction of cards that he gave away?
He gave away 9/12.
4. Julie had 35 blank computer disks that she wanted to share with her friends, Cindy and Jessie. She wanted to divide the disk among the three of them so that each one would have an equal amount. What is the fraction of disks that she would have left over?
She 2/35 left. Each of them would have 11 disks, which total 33. She would have 2 left.
5. Missy had a birthday party. She had a sheet cake that she could cut in 12 equal sizes. She wanted to invite 20 friends over for her birthday party. How many sheet cakes would she need if she friend received two pieces of cake? Would there be any cake left over? If so, what would the fraction be?
She would need four sheet cakes for her friends to have two pieces. She would have 8 pieces left. The fraction would be 8/48.
6. Missy had 2 pitchers of fruit punch for her birthday party. She could fill 24 cups using 1 pitcher. Would she have enough fruit punch so that each of her 20 friends could have a refill? If so, would she have any left? What fraction would she have left?
She could fill 48 cups. Each of her 20 friends could have a refill. She would have some left. She would have 8/48 left.
7. Carol had a large bag of candy that contained 169 pieces. She wanted to divide the candy into equal amounts with her friends, Susan and Megan. What fraction of candy would she have left after dividing the candy?
She could divide 169 by 3. She would have 1/169 left. Each one would get 15 pieces, and one left over.
8. Christy bought two bags of Christmas candy for $4.00. She gave the cashier $10.00. How much would she get back? What is the fraction of her money that she spent?
She would get back $6.00. She spent 4/10 of her money.
9. Beth had 96 pictures. She gave her two friends, Megan and Christy, 2/3 of her pictures, and she kept 1/3. How many pictures did Beth give away?
She gave away 2/3 of 96 = 64 pictures.
10. Bill had $135 that he collected from doing lawn work. His friends, Tom and Jim, helped with the lawn work, too. He needed to divide the amount equally. Would he have anything left over? If he did, what fraction is left?
He could divide $135 equally between the three of them. He would't have anything left over.