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# 13 2treediagram

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### 13 2treediagram

1. 1. Do I need a full closet? Using tree diagrams to show multiple outcomes
2. 2. Math Warm-up How many outcomes are in the sample space for each experiment? <ul><li>Flip a coin once </li></ul><ul><li>Flip a coin twice </li></ul><ul><li>Flip a coin three times </li></ul><ul><li>Roll a die once </li></ul><ul><li>Roll two dice </li></ul><ul><li>2 (h or t) </li></ul><ul><li>4 (hh, ht, th, or tt) </li></ul><ul><li>8 hhh, hht, hth, htt, tth, thh, tht, ttt)2x2x2 </li></ul><ul><li>6 1 </li></ul><ul><li>6 2 </li></ul>
3. 3. How many ways can he dress for success? <ul><li>Prof. Irish wears a different combination of shirt, tie, pants, and vest each day he teaches at the community college. </li></ul><ul><li>How many days can go by before he has to wear the same combination of clothing? </li></ul><ul><li>Prof. Irish is color blind so he doesn’t always know (or believe) that his color choices don’t always match. </li></ul>
4. 4. Pants, Ties, Shirts and Vests <ul><li>Pants </li></ul><ul><ul><li>Gray </li></ul></ul><ul><ul><li>Tan </li></ul></ul><ul><ul><li>Blue </li></ul></ul><ul><ul><li>Black </li></ul></ul><ul><li>Shirts </li></ul><ul><ul><li>Red </li></ul></ul><ul><ul><li>Brown </li></ul></ul><ul><ul><li>White </li></ul></ul><ul><li>Vests </li></ul><ul><ul><li>Blue </li></ul></ul><ul><ul><li>Tan </li></ul></ul><ul><li>Ties </li></ul><ul><ul><li>Bugs Bunny </li></ul></ul><ul><ul><li>Tazmanian Devil </li></ul></ul><ul><ul><li>Yosemite Sam </li></ul></ul><ul><ul><li>Texas Longhorns </li></ul></ul>
5. 5. Using a tree diagram Gray Tan Blue Black Each of the pants choices are listed, Each pair of pants can be matched with one of three colors of shirt: Red, brown, white
6. 6. Setting up a tree diagram Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White Notice that if there are three choices for each of the pants there will be 4x3 or 12 different combinations.
7. 7. 4 x 3 x 2 x ? Each of the twelve groups now can be paired with one of two vests. Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan We can now Add attach 4 ties to each Of the third list (vests) Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White
8. 8. How many combinations can be made? Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White bb td ys tl
9. 9. How many combinations can be made? Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan BB TD YS TxL Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl
10. 10. With just 13 articles of clothing… <ul><li>Prof Irish can dress differently every day of the semester. </li></ul><ul><li>He’ll still have some combinations left over. </li></ul><ul><li>How many combinations could be made if he purchased a second pair of shoes? </li></ul>
11. 11. How many clothing combinations could be made with… <ul><li>Two shirts, two pair of pants, and two pair fo shoes? </li></ul><ul><li>Three pair of pants, three pair of shoes, and two pair of shoes. </li></ul><ul><li>2x2x2= </li></ul><ul><li>3x3x2= </li></ul>
12. 12. Assignment <ul><li>Pg. 665 </li></ul><ul><li>#12-23 </li></ul>