Identify whether common events are certain, likely, unlikely, or improbable.

Statistics, Data Analysis and Probability: probability (certain, likely, unlikely, improbable) Some events are certain or likely to occur, whereas others are unlikely or improbable. Numbers can help us understand what situations might happen and what others might not.

Define probability: the likelihood or chance that an event will occur

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Can math help us understand what might or might not happen in the world? Yes, probability is a special type of math that helps us make predictions about events.

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How is probability written? Probability can be expressed as a fraction with the numerator being the total number of favorable outcomes, the denominator being the total number of possible outcomes.

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Can probability only be talked about in numbers? (No, another way to talk about probability is to use words like certain and unlikely.)

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If there are only three green M&M’s in your pocket and no others. How likely is it that you will get a green one if you reach in your pocket and pull out an M&M? (certain)

Children can use a spinner (spinner has different colors represented as different sizes on the spinner) to find the probability of spinning a particular color. Ask children which color they would rather choose. Have the child guess how many spins will end up the biggest color. Children can record their spins making a tally chart and compare it to the estimate made. Use the same prediction for twenty spins and see if the probability is closer to the child’s estimate. Another spinner can be made out of a paper plate and a paper clip and this time each color section can be made equal. Estimate probability, spin and record results. More spinners can be made with a greater number of equal sections and colors, too.

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Make a spinner and divide it into 8 sections. What’s the probability that the spinner will land on a number less than 4? (3/8) Make up similar questions for the child to answer.

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Children of this age are often not very flexible in their thinking. If, for example, if they remember receiving a particularly-enjoyed candy at a certain neighbor’s house while trick or treating at Halloween, they may assume that the same treat will be distributed at that house the following year. Try to use language when discussing recurring events with your children that allow room for the possibility, or probability, that experiences may vary, may change dramatically, or may not happen at all. Use terms such as “more likely” or “less likely” and help children explore reasons why a variety of experiences are probable in their lives. When a matter of health or well-being is involved, help them to determine the likelihood (probability) of a consequence occurring and to plan their reaction and/or responses accordingly. For example, if your teacher cannot read your paper, what is the probability that your teacher will ask you to do it over? How does this probability influence your actions?

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Offer your children real-life experiences that give them opportunities to experience probability and to make predictions for themselves. If, for example, your child has one pair of blue socks and several pairs of white socks, place the blue pair and several white pairs in a basket or box, ask your child to close his/her eyes and pick a pair of socks after predicting aloud how likely he/she thinks it is that the blue pair will be drawn. Put the pair drawn back and draw again. Continue until your child realizes that that so long as the same number of sock-pairs are in the basket, continued pulling a pair out does not increase the possibility of getting the blue pair. Then try this activity again, but when a pair is drawn don’t put it back in the basket. See if your child will notice that as the choice range narrows, the possibility of drawing a certain pair increases. Discuss how probability in this type of activity is all a matter of “luck” in that nothing the child does influences the outcome. It will happen on occasion that even with a hundred pair of white socks and only one blue that the blue ones will be drawn on the first try and you can discuss the odds of that happening. Listening to your child's reasoning when he/she explains his/her reaction to these events will help you understand the thinking process going on and give you an opportunity to expand that reasoning, as needed. Experiences such as these make it likely as your child matures he/she will engage in less and less “magical thinking” in which a child believes that he can influence events in which the real determiner of the outcome is chance.

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Many children’s board games offer structured opportunities to experience “chance” and help a child to separate his/her sense of self-worth/self-esteem from the outcome of the game. Examples of such games are those in which the play is determined only by chance—roll of dice, using a spinner, drawing a card at random, etc. Other games are won through the application of a specific skill; i.e., the game “Concentration” where some chance is involved, but an element of skill is present in that a child who can remember where specific cards were improves his/her chance of drawing that pair. Even in games that seem to be totally skill-based there is often a segment of chance: a game of who can call out the answer to the most addition facts before other players cab answer would seem to be a game of total skill, but in fact, chance determines which child gets a particular question and some will be easier than others. Discuss these situations with your child, choosing times when the child is not feeling “threatened” by the outcome of a recent game. Before playing any game, discuss how much chance plays a role in determining the outcome of the game. Encourage children to predict whether every player has an equal chance to win (a game of total chance) or whether skill plays a part. If skill is involved, how does that change children's predictions of the outcome? How can the odds be changed by modifying the rules or game pieces so that every child has some chance of winning? Opportunities to understand how chance changes the probability of certain outcomes helps children to make more informed choices in other areas of their lives and may reduce conflict when children play together.

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The games available to your child in this lesson, along with the Learning Tips that you can use to help children make maximum use of those games, are designed to help your child increase his knowledge and experience of a real-life reality: that there are elements of chance in the outcomes of many life experiences, and there are instances when skill and hard work are the determiners of success. They also set up the expectation that it would be useful to be able to estimate the likelihood of certain outcomes, and that is motivation for continuing the study of probability in future lessons. If your child needs extra help in understanding and using this basic knowledge of probability and chance, the most help that you can offer your child is not a worksheet but more opportunities to participate in real-life and simulated (games) activities such as are suggested in the Learning Tips and the computerized games provided in this lesson.

If you select a balloon without looking, how probable is it that you will get a red one? (draw a picture with 6 red balloons)

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If you select a balloon without looking, how probable is it that you will get a purple one? (include same picture as above)

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A bag contains 2 red, 3 blue and 4 purple marbles. Joseph draws one marble from the jar. What is the probability that Joseph will draw a purple marble? (4/9)

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What if Joseph draws again after drawing a purple marble out of the bag? (3/8)

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How many ways can you arrange a circle, square and triangle if you were to put them in a line?

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Henry has a green shirt, blue shirt and black shirt. He has brown pants, black pants and white pants. Make a diagram to figure out how many different combinations of shirt and pants Henry could make.

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Show a spinner with 8 sections, labeled 1-8.

What is the probability of the spinner landing on an even number.

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Show the same spinner.

What is the probability of the spinner landing on the number 8.

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Show a group of bowls with different numbers in them. The first has two 1’s, a 2 and a 3. The second has three 1’s and three 2’s. The third jar has one 1, two 2’s and one 3.

Which jar gives you an equally likely chance of pulling a 1 and a 2?

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Show a spinner divided into four quadrants, each a different color.

What is the likelihood that the spinner will land on blue? (1/4)

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Show the same spinner, but have two red quadrants.

What is the likelihood that the spinner will land on red? (1/2)

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You pull three coins out of your pocket. They add up to 51 cents. What is the likelihood that one of the coins is a penny? (100%//3/3)

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You flip a quarter. What is the likelihood that it will be heads when it lands? (1/2/50%)

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You flip a quarter. What is the likelihood that the tenth flip will be tails, if the other 9 flips have been heads? (1/2/50%)

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You roll a die. What is the probability that it will land on 5? (1/6)

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If you roll two dice. Does the probability change?

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Show a weather map of a week’s weather. It’s been sunny all week. Is it likely that it will be sunny tomorrow?

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Show ten yellow marbles. If you select a marble, how likely is it that it will be yellow?

(certain)

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Show ten yellow marbles. If you select a marble, how likely is it that it will be red?

(impossible)

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Show 6 coins: 5 quarters and 1 dime. If you reach in your pocket and select one of these coins, how likely is it that you will get a quarter? (probable)

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There are five cows and a rooster that live on a farm. How likely is it that you will get fresh eggs from the animals on the farm? (impossible)

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There are twenty students in your class and your mom brings 21 cupcakes for your birthday celebration. How likely is it that every child will get a cupcake? (very likely)

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If there are two doors to choose from, how likely is it that you will go through the right door. (50%/1/2)

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There are no more tryouts for the school play. You didn’t try out. How likely is it that you will be in the play? (unlikely)

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The sheep and the horse visit the pig outside the barn each day at noon. If you walk by the barn at lunchtime, how likely is it that you will see the pig? (very likely)