2. Welcome to Introduction to Bioinformatics Monday, 2 May 2005 Probability Anything you like How to read text files

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5. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers

6. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers 10 winners 42 97 222 247 356 667 713 801 8 numbers per card (50¢ each) 168 399 467 735 754 854 908 966 272 389 403 564 647 691 738 844 122 206 330 403 596 641 819 858 29 44 179 261 304 345 950 977

7. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 $ $ $ $ $ $ $ $

8. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability?

9. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability? 5

10. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability? 5 3

11. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability? 5 3 3

12. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1000 numbers 10 winners 8 numbers per card (50¢ each) 4 winners  $1,000,000 Probability? 5 3 3 1 2 3 2

13. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1 2 3 1. 1 2 4 2. 1 2 5 3. 1 3 4 4. 1 3 5 5. 1 4 5 6. 2 3 4 7. 2 3 5 8. 2 4 5 9. 3 4 5 10. How many possible cards? 10 How many winning cards? 6 Probability? 6 / 10 Probability The art of creative counting

14. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1 2 3 1. 1 2 4 2. 1 2 5 3. 1 3 4 4. 1 3 5 5. 1 4 5 6. 2 3 4 7. 2 3 5 8. 2 4 5 9. 3 4 5 10. Probability The art of creative counting But how to count when there’s too many to count?

15. Problem 9 Probability of choosing four correct numbers 2 1 3 4 5 2 1 3 5 4 2 1 4 3 5 2 1 4 5 3 2 1 5 3 4 2 1 5 4 3 2 3 1 4 5 2 3 1 5 4 2 3 4 1 5 2 3 4 5 1 2 3 5 1 4 2 3 5 4 1 2 4 1 3 5 2 4 1 5 3 2 4 3 1 5 2 4 3 5 1 2 4 5 1 3 2 4 5 3 1 2 5 1 3 4 2 5 1 4 3 2 5 3 1 4 2 5 3 4 1 2 5 4 1 3 2 5 4 3 1 3 1 2 4 5 3 1 2 5 4 3 1 4 2 5 3 1 4 5 2 3 1 5 2 4 3 1 5 4 2 3 2 1 4 5 3 2 1 5 4 3 2 4 1 5 3 2 4 5 1 3 2 5 1 4 3 2 5 4 1 3 4 1 2 5 3 4 1 5 2 3 4 2 1 5 3 4 2 5 1 3 4 5 1 2 3 4 5 2 1 3 5 1 2 4 3 5 1 4 2 3 5 2 1 4 3 5 2 4 1 3 5 4 1 2 3 5 4 2 1 4 1 2 3 5 4 1 2 5 3 4 1 3 2 5 4 1 3 5 2 4 1 5 2 3 4 1 5 3 2 4 2 1 3 5 4 2 1 5 3 4 2 3 1 5 4 2 3 5 1 4 2 5 1 3 4 2 5 3 1 4 3 1 2 5 4 3 1 5 2 4 3 2 1 5 4 3 2 5 1 4 3 5 1 2 4 3 5 2 1 4 5 1 2 3 4 5 1 3 2 4 5 2 1 3 4 5 2 3 1 4 5 3 1 2 4 5 3 2 1 5 1 2 3 4 5 1 2 4 3 5 1 3 2 4 5 1 3 4 2 5 1 4 2 3 5 1 4 3 2 5 2 1 3 4 5 2 1 4 3 5 2 3 1 4 5 2 3 4 1 5 2 4 1 3 5 2 4 3 1 5 3 1 2 4 5 3 1 4 2 5 3 2 1 4 5 3 2 4 1 5 3 4 1 2 5 3 4 2 1 5 4 1 2 3 5 4 1 3 2 5 4 2 1 3 5 4 2 3 1 5 4 3 1 2 5 4 3 2 1 1 2 3 4 51 2 3 4 5 1 2 3 5 4 How many total? How many possible cards of 3 from 5 numbers? x5 x4 x3 5! 1 2 3 4 5 1 2 3 5 4 1 2 4 3 5 1 2 3 4 5 1 2 3 5 4 1 2 4 3 5 1 2 4 5 3 1 2 5 3 4 1 2 5 4 3 1 3 2 4 5 1 3 2 5 4 1 3 4 2 5 1 3 4 5 2 1 3 5 2 4 1 3 5 4 2 1 4 2 3 5 1 4 2 5 3 1 4 3 2 5 1 4 3 5 2 1 4 5 2 3 1 4 5 3 2 1 5 2 3 4 1 5 2 4 3 1 5 3 2 4 1 5 3 4 2 1 5 4 2 3 1 5 4 3 2

16. Problem 9 Probability of choosing four correct numbers How many cards? How many possible cards of 3 from 5 numbers? 5! 2 1 3 4 5 2 1 3 5 4 2 1 4 3 5 2 1 4 5 3 2 1 5 3 4 2 1 5 4 3 2 3 1 4 5 2 3 1 5 4 2 3 4 1 5 2 3 4 5 1 2 3 5 1 4 2 3 5 4 1 2 4 1 3 5 2 4 1 5 3 2 4 3 1 5 2 4 3 5 1 2 4 5 1 3 2 4 5 3 1 2 5 1 3 4 2 5 1 4 3 2 5 3 1 4 2 5 3 4 1 2 5 4 1 3 2 5 4 3 1 3 1 2 4 5 3 1 2 5 4 3 1 4 2 5 3 1 4 5 2 3 1 5 2 4 3 1 5 4 2 3 2 1 4 5 3 2 1 5 4 3 2 4 1 5 3 2 4 5 1 3 2 5 1 4 3 2 5 4 1 3 4 1 2 5 3 4 1 5 2 3 4 2 1 5 3 4 2 5 1 3 4 5 1 2 3 4 5 2 1 3 5 1 2 4 3 5 1 4 2 3 5 2 1 4 3 5 2 4 1 3 5 4 1 2 3 5 4 2 1 4 1 2 3 5 4 1 2 5 3 4 1 3 2 5 4 1 3 5 2 4 1 5 2 3 4 1 5 3 2 4 2 1 3 5 4 2 1 5 3 4 2 3 1 5 4 2 3 5 1 4 2 5 1 3 4 2 5 3 1 4 3 1 2 5 4 3 1 5 2 4 3 2 1 5 4 3 2 5 1 4 3 5 1 2 4 3 5 2 1 4 5 1 2 3 4 5 1 3 2 4 5 2 1 3 4 5 2 3 1 4 5 3 1 2 4 5 3 2 1 5 1 2 3 4 5 1 2 4 3 5 1 3 2 4 5 1 3 4 2 5 1 4 2 3 5 1 4 3 2 5 2 1 3 4 5 2 1 4 3 5 2 3 1 4 5 2 3 4 1 5 2 4 1 3 5 2 4 3 1 5 3 1 2 4 5 3 1 4 2 5 3 2 1 4 5 3 2 4 1 5 3 4 1 2 5 3 4 2 1 5 4 1 2 3 5 4 1 3 2 5 4 2 1 3 5 4 2 3 1 5 4 3 1 2 5 4 3 2 1 1 2 3 4 5 1 2 3 5 4 1 2 4 3 5 1 2 4 5 3 1 2 5 3 4 1 2 5 4 3 1 3 2 4 5 1 3 2 5 4 1 3 4 2 5 1 3 4 5 2 1 3 5 2 4 1 3 5 4 2 1 4 2 3 5 1 4 2 5 3 1 4 3 2 5 1 4 3 5 2 1 4 5 2 3 1 4 5 3 2 1 5 2 3 4 1 5 2 4 3 1 5 3 2 4 1 5 3 4 2 1 5 4 2 3 1 5 4 3 2 1 2 3 4 5 1 2 3 5 4 2 1 3 4 5 2 1 3 5 4 3 1 2 4 5 3 1 2 5 4 2 1 3 2 4 5 1 3 2 5 4 2 3 1 4 5 2 3 1 5 4 3 2 1 4 5 3 2 1 5 4 · 3! (CHOOSE 5 3)

17. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1 2 3 1. 1 2 4 2. 1 2 5 3. 1 3 4 4. 1 3 5 5. 1 4 5 6. 2 3 4 7. 2 3 5 8. 2 4 5 9. 3 4 5 10. How many possible cards? 10 How many winning cards? 6 Probability? 6 / 10 Probability The art of creative counting (CHOOSE 5 3)

18. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1 2 3 1. 1 2 4 2. 1 2 5 3. 1 3 4 4. 1 3 5 5. 1 4 5 6. 2 3 4 7. 2 3 5 8. 2 4 5 9. 3 4 5 10. How many possible cards? How many winning cards? 6 Probability? 6 / 10 Probability The art of creative counting (CHOOSE 5 3) (CHOOSE 3 2)

19. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 1 2 3 1. 1 2 4 2. 1 2 5 3. 1 3 4 4. 1 3 5 5. 1 4 5 6. 2 3 4 7. 2 3 5 8. 2 4 5 9. 3 4 5 10. How many possible cards? How many winning cards? 6 Probability? 6 / 10 Probability The art of creative counting (CHOOSE 5 3) (CHOOSE 3 2) *(CHOOSE 2 1)

20. Problem 9 Probability of choosing four correct numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210... 991 992 993 994 995 996 997 998 999 1000 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability?

21. Problem 9 Probability of choosing four correct numbers 1000 numbers 10 winners 8 numbers per card (50¢ each) 29 44 179 261 304 345 950 977 4 winners  $1,000,000 Probability? Number of winning cards Number of total cards (CHOOSE 10 4) (CHOOSE 1000 8) (CHOOSE 990 4) Number of winning cards Probability of one winning card *