This document discusses two probability questions involving the arrangement of strawberries pinned to a wall. Part I asks for the number of arrangements if five leafed strawberries remain together. There are seven possible arrangements. Part II asks for the probability of selecting a leafless berry with a green pin followed by a leafed berry with a yellow pin, without replacement. A tree diagram is constructed to calculate the probability as 1/2.

1. JUDE’S DRAFTING TABLE The Strawberry Question

2. THE QUESTION: For an art piece, strawberries were pinned to a wall. On the first row, six out of the eleven strawberries had a yellow pin that supported them in place. The rest of them were held up by green pins . Five of these eleven strawberries had the crown of leaves that grew on top.

3. THE QUESTION: PART I (a) In how many different ways could the strawberries be arranged if the leafed strawberries remained together?

4. .:. WHAT WE KNOW .:. six out of eleven strawberries had yellow pins 11 – 6 = 5; five remaining strawberries had green pins five strawberries had crown of leaves on top six strawberries were leafless

5. THE SOLUTION: PART I a rough diagram helps show the slots. it is important to know that leafed and leafless strawberries are both classified as non-distinguishable objects. the leafed strawberries take up five slots and must be together; this can be done in seven arrangements of five. STEPS PROCESS

6. THE QUESTION: PART II (b)If the eleven strawberries from the original batch were placed into a separate container, what was the probability of getting first a leafless berry with a green pin followed by a leaved strawberry with a yellow pin if they are not replaced?

7. THE SOLUTION: PART II Since there are non-distinguishable objects involved; coloured pins and leafed/leafless strawberries, and also involves probability, a helpful tool would probably be a diagram. Specifically a labelled tree diagram. STEPS

8. THE TREE DIAGRAM

9. 5/11 6/11 5/11 5/11 6/11 6/11 4/10 = 2/5 6/10 = 3/5 5/10 = ½ 4/10 = 2/5 6/10 = 3/5 5/10 = ½ 5/10 = ½ 5/10 = ½ ½ ½ ½ ½ 2/5 2/5 2/5 2/5 2/5 ½ ½ ½ ½ 2/5 2/5 2/5 LEAFLESS LEAFLESS LEAFLESS LEAFLESS LEAFLESS

10. STEPS SOLUTIONS CONT’D… How to construct the tree diagram would be to label all of the possibilities of each turn and then label them with the exact value they are given. After the table is constructed, most of the hard work is done, all that is left to do now is to select the branch with the specific outcomes that are asked to be found. For this question, P (leafless green, leafed yellow) Once the branch is selected, multiply the exact values to get the probability.

11. PROCESS

12. .:. STRAWBERRY FIELDS FOREVER .:. Let me take you down/‘Cause I’m going to Strawberry Fields/Nothing is real/And nothing to get hung about/ Strawberry Fields Forever /Living is easy with eyes closed/Misunderstanding all you see/It’s getting hard to be someone but it all works out/It doesn’t matter much to me/Let me take you down/‘Cause I’m going to Strawberry Fields/Nothing is real/And nothing to get hung about/ Strawberry Fields Forever /Always no sometimes/Think it’s me/But you know I know when it’s a dream/I think I mean “yes,” but it’s all wrong/That is I think I disagree/Let me take you down/‘Cause I’m going to Strawberry Fields/Nothing is real/And nothing to get hung about/Strawberry fields forever. Strawberry Fields Forever by flickr user Rodrigo Vera