>> << 12 0 obj 199 0 obj <>/Filter/FlateDecode/ID[<7A5A2F2C6F86A14C9564B82DF3B46C77><9CE1FBB2A2C54649A07B0F4D1A8497C9>]/Index[193 15]/Info 192 0 R/Length 53/Prev 21743/Root 194 0 R/Size 208/Type/XRef/W[1 2 1]>>stream /A 11 0 R PROBABILITY & TREE DIAGRAMS Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. 5. Instructions Use black ink or ball-point pen. /H /I (The trees are provided between the questions and the answers.) Some of the worksheets for this concept are Kuta software probability, Tree diagrams 70b, Awork aboutprobabilitytreediagrams, Tree diagrams and probability, Mathematics linear 1ma0 probability tree diagrams, Tree diagrams and the fundamental counting principle, Wjec mathematics, Probability tree diagrams. endstream endobj startxref endobj Try to answer all the questions marked (a), (b), etc... 6. Double check that the leaf probabilities add to one. /F2 8 0 R /Length 15 0 R /URI (http://www.pdffactory.com) << >> >> endobj Conditional Probability and Tree Diagrams De nition If A and B are events in a sample space S, with P(B) 6= 0, the conditional probability that an event A will occur, given that the event B has occurred is given by P A B = P(A\B) P(B): If the outcomes of S are equally likely, then P A B = endobj endobj stream c. /Rect [262.08 22.86 367.44 9.06] << << Œ†Ùr$ØàOÃaE‰ÿ¹R¢Dİ¥²„Ù|›}‡ÙëhŒsÜŒH/~‚J�C¢›¬çõÒÒ«WCXóí‘g7w¨BHÃkï‘¢„qnaMàÛ.kĞ9sf¼¡.„Ò8$»õ2PÔ™Ñ&a‰4Âü_Âb­µ3�%§DËÍúí /A 13 0 R 8. endobj >> The tree diagram for randomly picking three blocks without replacement, with associated probabilities, would look like this: B B= B Y Y1 Y Y B3 B Y B1 H‰­VÛn1}ç+汕Šc{½^ïkERT)RÕğ$BÄ%‚%¨ß™±½x/lò�{f||æâ±Üƒ$üıJg°r%a;¢Aî`3*” £‡‘‚W@í=J²*´¤é~ÎF7w e|u������{뷻귴�����N\8Y�������ۼT����f����n��_�L9������I#�s�ݗ�{��~����rt����?��)�Ia��9����D��0 �4 �AflQ�Fߒ�'�Q��6R�!�����A�X�X|F]m�0�y�;�'~h!�SS,�E�� �؂cn��l��czf}��@M�������BkI��֥�qE|�� �5�� -ɍ�v=�V)@Gش�z �1��.�}�8�Ҡ���;f��?�7�+i.�)% 13 0 obj /Parent 3 0 R In a conditional probability an outcome or event E is dependent upon another outcome or event F. A box contains 3 blue blocks and 2 yellow blocks. /Subtype /Link << >> /Type /Page /Resources Math 130 Worksheet 8 Using Tree Diagrams Names _____ 1. 2. 0 /Annots 9 0 R /Font /Rect [262.08 20.64 369.36 9.36] Displaying top 8 worksheets found for - Probability Tree Diagrams. /Filter /FlateDecode Worksheet containing the examples. %%EOF << /MediaBox [0 0 792 612] /S /URI %PDF-1.5 %���� Check your tree against mine. << 3. Originally used for a GCSE Higher tier set. endobj /Type /Annot ������8�)2L�|�G��&����� ���z�)YF�G�R�/@���O�+�9��v�v�. >> /Type /Annot RV�f�=]n^V���]߮? Añã§%¬)eAëw2ëŠuñWFHseb‘ ¼&±”)KüuÉÑä®ùÒÑ ÷î¬zúÀk°éϽ8eA‚; a. << Finding Probability Using Tree Diagrams and Outcome Tables Chapter 4.5 –Introduction to Probability PDF created with pdfFactory Pro trial version www.pdffactory.com. 7. 207 0 obj <>stream 14 0 obj 193 0 obj <> endobj endstream endobj 194 0 obj <>/Metadata 13 0 R/Outlines 24 0 R/PageLayout/OneColumn/Pages 191 0 R/StructTreeRoot 27 0 R/Type/Catalog>> endobj 195 0 obj <>/Font<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 196 0 obj <>stream Congratulate self. Represent the sample space for this problem by a tree diagram. h�bbd``b`� �SA�+ �� $Xw�ϖL�@#n�?#�/� n� /S /URI ^ğ¢Úë�Rìõ:‹«šL-:×yáã´Na?>ëQâÅ>8 pœ_(g½~;Ÿç”Úª�ÁË"hœqSy±æm. >> 10 0 obj endobj 4. 3. endobj [10 0 R 12 0 R] /H /I b. 581 11 0 obj Check all those answers in the back of the worksheet. 5 0 obj h�ԗKo�6�����!�ޒ��Iڠ�A� v9����G0�E���$-ʲg٢HQ����Rh�����B;��� V(oQㄎ /Border [0 0 0] Tracing paper may be used. h�b```�Df�e���af`a�pbP�`0WXðY������s20�[i f�x���`!oc� ��b`�LҌ@�������q\��������� � h� /Subtype /Link Draw a probability tree diagram. /ProcSet [/PDF/Text] Tree Diagrams n if you flip a coin twice, you can model the possible outcomes using a tree diagram or an /Border [0 0 0] What is the probability that they end up with two boys? 9 0 obj Resources included: 1. /Contents 4 0 R SMART notebook lesson. ~�F�؇����U�o��2������U���v�%���������ޛ�vP]��U��V7�Mu����¹H:�BB���i����w�ݺ݋���q�n6ߓ�Y�i@A���]\mWϿܓ��ߵ��ku�ݭ�u}" 6 0 obj ØÙÍá^ʳH¡§m™a|Ëõç¯4ãn®^P„ê�IŞ„ı¸®/s•N;1ofC º™€wVM+ñçõ�ıKõAe§Oò6Ç�™ƒ0Ÿ.©”Ü]EßêsoÉ"›6¿WÈÂÍŒ‡Ü»™îş¿ny:ØQâî¹ìgÿkî\Àë¿äœ%8:¥–Æ‚©4óö^§f¬¸½™¡“ñìÍt“×…/XfbR& …¶%ì¢%½…endstream /URI (http://www.pdffactory.com) >> A couple plans to have two children. For each child it is equally likely to be a boy or a girl. 2. /F1 7 0 R