Explore It! Find a Sample Space. Activity 1. Name Class Date. Sample Spaces

Size: px

Start display at page:

Download "Explore It! Find a Sample Space. Activity 1. Name Class Date. Sample Spaces"

Naomi McCormick
7 years ago
Views:

1 Name Class Date Explore It! Sample Spaces Find a Sample Space The set of all possible outcomes of a probability experiment is called the sample space. The sample space may be quite small, as it is when you toss a coin (sample space: heads or tails). Activity 1 A number cube is numbered from 1 to 6. A spinner has 5 equal sections lettered from A through E. You can use an organized list to find the sample space for an experiment. Work with a partner. Decide on a logical system you can use to list all the possible outcomes when you roll the number cube and spin the spinner. Describe the method you will use. Write the sample space. Use a number and a letter to write each possible outcome. For example, 3B means Roll a 3, spin a B. 3. How many outcomes are there in the sample space? 1 of 5

2 Try This Suppose that instead of rolling a number cube in Activity 1, you tossed a coin. a. Write the sample space for tossing a coin (H = heads, T = tails) and spinning a spinner lettered from A through E. b. How many items are there in the sample space? Sample spaces are easy to find in the real world. You may even have one in your own closet! Activity 2 What would happen if you randomly chose your clothes in the morning? What pants-shirt combinations are possible outcomes? 3. Work with a partner again. Decide on a system you can use to list all the possible pants-shirt outfits if you have the clothes shown above. Describe the method you will use. In the space below, write the sample space. Use two letters to write each possible outfit. For example, JS means jeans and sweater. What if you could wear each outfit with either brown shoes or black shoes? Without listing the sample space, explain how you could find the number of possible pants-shirt-shoe outfits. How many are there? 2 of 5

3 Try This Ingrid is sending out thank you cards for birthday presents. She has pink, blue, and green cards, and white and yellow envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Draw Conclusions 3. In Try This 2, you found the sample space for three types of cards and two types of envelopes. What operation seems to relate three options and two options to the size of the sample space? 3 of 5

4 Answer Key Goal Applying the strategy Make an Organized List, students count the possible outcomes of two probability experiments, using logical thinking to prepare themselves to understand and use formal counting methods. Teaching Tips For each activity, emphasize the use of an organized counting system. Explain that listing possible outcomes randomly will take longer and will likely miss one or more outcomes. For Activity 2, for example, suggest that students focus on one top at a time with each of the different pants. Connect this topic back to probability by explaining that finding the probability of an outcome requires that you know how many different ways an event can occur. Activity 1 Possible answer: Start with List 1 with each of the 5 possible letters. Repeat with 2, 3, 4, 5, and 6 in succession. 1A, 1B, 1C, 1D, 1E, 2A, 2B, 2C, 2D, 2E, 3A, 3B, 3C, 3D, 3E, 4A, 4B, 4C, 4D,4E, 5A, 5B, 5C, 5D, 5E, 6A, 6B, 6C, 6D, 6E Try This a. HA, HB, HC, HD, HE, TA, TB, TC, TD, TE b. 10 Building Conceptual Understanding Ensure that students can list all the possible outcomes of simple probability experiments using informal methods such as making an organized list or using logical thinking. Describe an organized method you could use to list all the possible outcomes if your toss a coin (H, T) and roll a number cube (1, 2, 3, 4, 5, 6). How many possible outcomes are there? Possible answer: Start with H. Pair it with each possible number cube outcome (H1, H2, H3, H4, H5, H6). Repeat, pairing T with each possible number cube outcome (T1, T2, T3, T4, T5, T6); 1 Close Adam, Brynn, and Cody (A, B, C) are running for class president. Dawn, Errol, and Fritz (D, E, F) are running for vice-president. List all the possible president/ vice-president outcomes. How many are there? AD, AE, AF, BD, BE, BF, CD, CE, CF; 9 4 of 5

5 Activity 2 Possible answer: Start with pants. List J with each of the 3 possible shirts. Repeat with K. JT, JB, JS, KT, KB, KS 3. There are 12 pants-shirt outfits now. When I add shoes, there will be 6 outfits matched with black shoes and 6 outfits matched with brown shoes,for a total of 12 possible outfits. Try This PY, PW, GY, GW, BY, BW Draw Conclusions 3. Possible answer: There are 6 options in the sample space, and you can also get that answer by multiplying 3 and 5 of 5

PROBABILITY. SIMPLE PROBABILITY is the likelihood that a specific event will occur, represented by a number between 0 and 1.

PROBABILITY. SIMPLE PROBABILITY is the likelihood that a specific event will occur, represented by a number between 0 and 1. PROBABILITY SIMPLE PROBABILITY SIMPLE PROBABILITY is the likelihood that a specific event will occur, represented by a number between 0 and. There are two categories of simple probabilities. THEORETICAL