Question

Ginny is deciding whether to spend all day Saturday studying Herbology. If she studies, she has a 40% probability of earning an A, 40% probability of earning a B, and 20% probability of earning a C. If she does not study, she has a 10% probability of earning an A, a 50% probability of earning a B, and 40% probability of earning a C. She values a free Saturday at $70, an A at $200, a B at $100, and a C at -$70. Create a decision tree to help Ginny decide. Label parts of the tree. State what Ginny should do and why. Her risk tolerance is $50

Answer 1

Refer following screenshot for the solution. Ginny is better off not studying as the probability weighted gain of not studying is $ 112 while that of studying is $ 106. However, note that in all three circumstances, the actual gain under each scenario is higher by not studying.

Decision Tree.xlsx - Excel Tell me what you want to do... 0 x & Share Data Review View 0 - Sign in Ay O Power Pivot === Wrap Text General + x Autosum Fill - SSY Jabe File Home Insert Page Layout Formulas Cut Arial -9 -A A ES Copy - Paste B I U , - >> A, Format Painter Clipboard Font A1 : X for A B C D E E Merge & Center, $ % 48.08 Insert Delete Format Conditional Format as Cell Formatting Table Styles Styles Clear Sort & Find & Filter Select Editing Alignment Number Cells F G H I J K L M N O P Q R S I A 40% * 200 =$ 80 She will actually make $ 200 here Choose 40% * 100 = $ 40 Total Value derived by studying = $ 80 + $ 40-$ 14.= $ 106 study She will actually make $ 100 here Start with the day 20% -$ 14 She will actually make - $ 14 here WONOASSORDHAURO VOOWN 000000 She will actually make $ 270 here 10% * 200 = $20 Choose not to study She will actually make $ 170 here 50%* 100 = $.50 Total Value derived by not studying = $ 20 + $ 50 - $ 28 + $ 70 (free saturday).= 112 She will actually make $ 42 here 40% *-70 -$28 Sheet1 Ready O -- 90% + 9:52 AM 28/03/20205 3/2020 X A 4x