XYZ Mat 120 Module 2 Lesson 2 1 Part 1 — Transcript

Full transcript

1. 0:00this is module 2 lesson 2.1
2. 0:03on probability some terms
3. 0:06to start off with that we need to know
4. 0:11our event which is our desired outcomes
5. 0:15what do we want to happen
6. 0:16a simple event is just simply one
7. 0:18outcome
8. 0:19and a sample space that's something
9. 0:21we're going to use a lot all possible
10. 0:23simple events
11. 0:24everything that could possibly happen so
12. 0:27some examples of this
13. 0:29would be tossing a coin if you toss a
14. 0:32coin
15. 0:32you're going to either get a head or a
16. 0:34tail that's going to be the sample space
17. 0:36the event what do you want to happen we
18. 0:39might get a head
19. 0:40or we might get a tail either one of
20. 0:42those could be events
21. 0:44if we toss two coins we have more
22. 0:46outcomes
23. 0:47we'll have a head on the first toss and
24. 0:49a head on the second toss
25. 0:51a head on the first toss and a tail on
26. 0:53the second toss
27. 0:54a tail on the first one and then a head
28. 0:56or a tail in the tail so there are four
29. 0:58different outcomes
30. 0:59event what's the probability of getting
31. 1:01two tails
32. 1:03you could say what's the probability of
33. 1:04getting two heads or what's the
34. 1:06probability of getting a head and a tail
35. 1:08then we roll dice one die it's called a
36. 1:12die
37. 1:13there's six sides if it's a standard die
38. 1:16so you could get a one or a two or three
39. 1:18or four five or six
40. 1:20what's the probability you roll an even
41. 1:21number what's the probability you roll
42. 1:23an odd number so lots of things you can
43. 1:25ask
44. 1:26but then look at this when you roll two
45. 1:28dice then you have
46. 1:29lots of possibilities a one and then a
47. 1:32one
48. 1:32a two and then a one a three and then a
49. 1:34one and you keep on going on and you
50. 1:36have 36 different possibilities when we
51. 1:39roll two dice
52. 1:40what's the probability you get a sum of
53. 1:42seven so what are the numbers that add
54. 1:44up to seven
55. 1:45six and one five and two four and three
56. 1:48three and four
57. 1:49two and five and six and one you notice
58. 1:52that these
59. 1:54should be
60. 1:57these should be ordered what you get on
61. 2:00the first roll and then
62. 2:02what do you get on the second roll
63. 2:05complement
64. 2:05the complement looks like this it is a
65. 2:08with a bar
66. 2:09over it and that means all outcomes that
67. 2:11are not in a
68. 2:12a and a complement add up to one
69. 2:16so if the probability of a is 0.75
70. 2:19then the probability of a complement is
71. 2:211 minus 0.75
72. 2:23or 0.25 and let's look at an example
73. 2:27a poll showed that 70.1 percent of
74. 2:30americans say they believe statistic
75. 2:31teachers know the true meaning of life
76. 2:33what's the probability
77. 2:34of selecting someone who does not
78. 2:36believe this
79. 2:37so what is the complement so in order to
80. 2:40do that
81. 2:42we'll just say that would be 70.1
82. 2:45percent
83. 2:46so clear all this out that would be 1
84. 2:49minus
85. 2:520.701
86. 2:54and that would be 0.299 that would be
87. 2:5629.9
88. 2:57percent so i'm going to write that as a
89. 2:59percentage
90. 3:00so 29.9 percent
91. 3:05and we just subtracted 70.1 from 1.
92. 3:09classical probability classical
93. 3:11probability
94. 3:12is the main type of probability that
95. 3:14uses numerical values you have the
96. 3:17number of ways of
97. 3:18an event can occur divided by the total
98. 3:20number of events that are possible
99. 3:23sometimes we'll have fractions we want
100. 3:24them reduced if we have decimals we want
101. 3:27two or three places
102. 3:28and probability ranges from zero to 1.
103. 3:33and then here's an example what
104. 3:36could be a probability well if
105. 3:39probability is between
106. 3:410 and 1 what is the square root of 2
107. 3:45oh that's more than one so that one
108. 3:47cannot be a probability
109. 3:49but one can be a probability
110. 3:52what's the square root of one half well
111. 3:55you might not know these things so let's
112. 3:57do the square root of one divided by 2
113. 4:01and that is less than 1. so that one
114. 4:03could be
115. 4:04a probability what is 13 divided by 29
116. 4:10well that one is 0.44 that one could be
117. 4:12a probability
118. 4:14and the 0.25 a 2 also could the only one
119. 4:18that could not in this set is the square
120. 4:19root of 2
121. 4:20because the probability ranges
122. 4:24between 0 and 1. it can equal 0
123. 4:28and it can equal 1.
124. 4:31look at our dice we have 6 cited die
125. 4:35and we want to find the probability we
126. 4:37get
127. 4:38a 2. well remember our sample space
128. 4:41is all of the outcomes on the die
129. 4:44well there's only one two so it's two
130. 4:47out of
131. 4:48six um so
132. 4:52two out of six should be one third
133. 4:56the number showing is a two two out of
134. 4:59six would be one out of six i'm sorry
135. 5:01so we've got one out of six not two out
136. 5:04of six one out of six because we only
137. 5:06have one two there
138. 5:08an even number well the even numbers
139. 5:12are two four and six so we have three of
140. 5:15them
141. 5:15so we have three out of six we're going
142. 5:17to write that as one-half
143. 5:19and then a number greater than three so
144. 5:21anything greater than three
145. 5:23would be a four five or six and again
146. 5:26that's three possibilities out of six
147. 5:28so that gives me one half
148. 5:32then when we do the sums this goes back
149. 5:34to what i was looking at just a minute
150. 5:35ago where i did the one and the one and
151. 5:36the one and the 2 and the 1 and the 3.
152. 5:38this shows you a picture what's the
153. 5:40probability of getting the sum of 5.
154. 5:42now how can i get a 5 i can get it with
155. 5:45a 4 and a 1
156. 5:46with a 1 and a 4 with a 3 and a 2
157. 5:50with a 2 and a 3. those are the only
158. 5:52ways i can get 5.
159. 5:53if you count all of these combinations
160. 5:55it was a total of 36.
161. 5:57so the total is always going to be my
162. 5:59denominator
163. 6:00so i have four different ways out of 36.
164. 6:05so 4 out of 36 would be reduced
165. 6:08to 1 over 9. now what's the probability
166. 6:11of getting doubles
167. 6:12well doubles would be a 1 and a 1 a 2
168. 6:15and a 2
169. 6:16a 3 and a 3 4 and a 4 five and a five
170. 6:20and a six and a six so that's six
171. 6:22different things
172. 6:24out of 36 so that would be reduced to
173. 6:27one out of six
174. 6:29and then a sum more than ten so more
175. 6:32than ten
176. 6:33well a 6 and a 6 gives me 12. a 6 and a
177. 6:375 gives me 11.
178. 6:38a 5 and a 6 gives me an 11 and then
179. 6:42everything else would be 10 or less so
180. 6:45more than 10 would be 11 or 12 so
181. 6:48they're three ways out of 36
182. 6:50so that would be one over 12.
183. 6:55and then another example this is from
184. 6:57your homework
185. 6:58you've got pennies nickels dimes and
186. 7:00quarters and so
187. 7:02we want to know what is the total here
188. 7:05so if i take
189. 7:06all of these and add them together i
190. 7:08have 19
191. 7:09plus 33 plus 41
192. 7:13plus 42 have a total of 135
193. 7:16so my total is 135
194. 7:21that's equal to the total and
195. 7:25then we're going to find the probability
196. 7:28that the coin is a penny so
197. 7:30here are my pennies pennies are 19 so 19
198. 7:33out of 135
199. 7:35and it says round to three decimal
200. 7:38places
201. 7:39so i'll just do 19 out of 135
202. 7:43round that off to 0.141
203. 7:49then what's the probability we get a
204. 7:50dime okay go over here and look at your
205. 7:52dimes
206. 7:53we have 41 of them so 41 out of 135
207. 7:5841 out of 135
208. 8:02rounded to three decimal places is 0.304
209. 8:06so we'll write that as 0.304
210. 8:10and then the probability that it's not a
211. 8:12nickel so if it's not a nickel
212. 8:14well the nickels you've got 33 of them
213. 8:17not
214. 8:18a nickel would be everything else so i
215. 8:20have 19 pennies
216. 8:23i have 41 dimes and i have 42 quarters
217. 8:27so not a nickel that would be 102
218. 8:29possibilities
219. 8:31out of 135
220. 8:34still my total is always the total 135
221. 8:37and three decimal places would be 0.756
222. 8:42so 0.756
223. 8:47so that is part 1 of
224. 8:50module 2 lesson 2.1.