Topic 8 Unit 2- Uncertainty 74 Basic Probability Tools (cont.) Activity 8.1: Two-Dice Rolls-Word Seareh Event Search In the game Roller Derby, we only cared about the sum of the dice on each roll, but there are other ways to describe outcomes when rolling two dice. Here we are looking more broadly at events that occur in an experiment where we roll two dice. We are going to study the sample space of two-dice outcomes and do an "event search". This will be a bit like a word search, but we'll be circling or shading events. White (2nd) Die Outcomes Remember, that an event is a subset of the sample space. Try to find the following events in the sample space above. Mark all of outcomes that make up an event by circling or cross-hatching with a colored pencil. Be prepared to share and defend your choices. In each case, tell whether the event is impossible, possible-but-not-certain, or certain. Calculate the probability of that event. Event Probability Color Status? Coding A: Sum of the dice is 4 P(A) = 6 B:Black (1st) die is 1 P(B)b/36 Р В) 11 C: Outcomes that are simultaneously in A and B P(C) = P(A and B) =|36 P(D)=6 P(E) = P(A and D) D:White (2nd) die is 4 E:Outcomes that are simultaneously in A and D F: Sum of the dice is 12 or less P(F) = G: Sum of the dice is 1 P(G) = H:Sum of the dice is less than 9 P(H) 26 36 1 I: Sum of the dice is 9 or greater PO=1036 P(J) = P(Hor I) = P(K) = P(B or D) = \\3b P(L) = P(D or I) = 6 J:Outcomes that are in H or I (okay to be in both) K: Outcomes that are in B or D (okay to be in both) 11 11 L:Outcomes that are in D or I (okay to be in both) 1 Black (1st) Die Outcomes .. experiments the circumstances that would give similar results. 6. Events J, K, and L are each described similarly - as sets in which the outcomes are in one or the other (or both) of two other events. There is actually a mathematical relationship - an equation - that ,relates four different probabilities in each of these cases. Complete the table below and describe what seems to be consistently happening in each case. Do you see the equation in each case? а. Event L Event K Event J Events of the D or I B or D Hor I form A or B P(D)= P(I)= P(D and I) = P(D or I) = P(B) P(D) = P(B and D)= P(B or D) = always include outcomes that P(H)= P(I)= P(H and I) P(H or I) = II 11 just in A, just in B, or in both sets are 1 simultaneously. might this happen Is this equation a coincidence with these three cases for this experiment, or similarly in other experiments? Explain in such a way that a skeptic would be convinced. b.