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Conditional probability

A local beer producer sells two types of beer, a regular brand and a light brand with 30% calories. The company's marketing department wants ti verify that its traditional approach of appealing to local white collar workers with light beer commercials and applealing to local blue-collar workers with regular beer commercials is indeed a good strategy. A randomly selected group of 400 local workers are questioned about their beer-drinking preferences, and the data in the file P05_08.xlsx are obtained.
a. If a blue-collar worker is chosen at random from this group, what is the probability that he or she prefers light beer(to regular beer or no beer at all)?

b. If a white-collar worker is chosen at random from this group, what is the probability that she or he prefers light beer(to regular beer or no beer at all)?
Worker Type Preference
1 B R
2 W N
3 W L
4 B R
5 B R
6 B R
7 B L
8 B L
9 B R
10 B L
11 B L
12 B L
13 W L
14 B L
15 W R
16 B R
17 B L
18 W R
19 B R
20 W L
21 B R
22 W R
23 B L
24 B L
25 B R
26 B R
27 B N
28 W L
29 B R
30 W L
31 W R
32 B R
33 B N
34 B L
35 B L
36 W L
37 B R
38 W R
39 B R
40 B L
41 B R
42 B L
43 W L
44 B L
45 W N
46 W N
47 W L
48 B R
49 B R
50 B L
51 W L
52 B N
53 B R
54 W L
55 B R
56 W R
57 W R
58 B R
59 W L
60 B L
61 W R
62 B R
63 B L
64 W R
65 B R
66 B R
67 W R
68 W L
69 B R
70 W R
71 B L
72 B L
73 W L
74 B R
75 W R
76 B L
77 W L
78 B R
79 B L
80 W L
81 B R
82 B L
83 B L
84 B L
85 B R
86 W R
87 W L
88 W L
89 B L
90 B L
91 W L
92 B R
93 W R
94 B L
95 B R
96 W N
97 W L
98 B L
99 W L
100 B R
101 W R
102 B N
103 B L
104 B R
105 B L
106 W L
107 B R
108 B R
109 B L
110 B L
111 B R
112 B L
113 W R
114 W R
115 B R
116 B L
117 W L
118 B R
119 B L
120 B L
121 B L
122 W R
123 W R
124 B R
125 W L
126 B R
127 B L
128 B L
129 W R
130 W L
131 W L
132 B L
133 B L
134 W L
135 B R
136 B L
137 B R
138 B L
139 B L
140 W L
141 W L
142 B L
143 B L
144 B R
145 W R
146 W L
147 B L
148 B R
149 B N
150 B L
151 B N
152 B L
153 W L
154 B R
155 W R
156 W N
157 W L
158 B L
159 B L
160 B R
161 B L
162 B L
163 B R
164 B R
165 W R
166 B R
167 W L
168 B R
169 B R
170 B L
171 W L
172 B L
173 B L
174 W L
175 W R
176 B L
177 B N
178 W L
179 B L
180 W L
181 W N
182 B L
183 W R
184 B L
185 W R
186 B L
187 B R
188 B R
189 B R
190 W L
191 W R
192 W L
193 W L
194 B R
195 B L
196 B R
197 W R
198 B R
199 B L
200 B L
201 W R
202 B N
203 W R
204 B L
205 B L
206 B N
207 W R
208 B L
209 B R
210 B L
211 B R
212 B L
213 B R
214 W R
215 W R
216 W R
217 W L
218 W R
219 B R
220 W R
221 B L
222 W L
223 W L
224 B R
225 W N
226 B L
227 W R
228 W L
229 B L
230 B R
231 B N
232 W R
233 W L
234 B R
235 W L
236 B L
237 B L
238 B R
239 B R
240 W R
241 W R
242 W R
243 W L
244 B L
245 W R
246 W L
247 B R
248 B R
249 B L
250 W R
251 W L
252 B N
253 B R
254 W L
255 B L
256 B R
257 B L
258 W L
259 B R
260 B R
261 B L
262 B L
263 B R
264 B R
265 W N
266 W R
267 B L
268 B L
269 B R
270 B L
271 B L
272 B L
273 B R
274 B R
275 B R
276 B R
277 W R
278 B N
279 W L
280 B N
281 B L
282 W R
283 B R
284 B R
285 B R
286 W L
287 B L
288 W L
289 W R
290 W L
291 W L
292 B R
293 B N
294 B R
295 B R
296 B R
297 B L
298 B R
299 B R
300 W N
301 B R
302 W L
303 B R
304 B L
305 B R
306 B R
307 B R
308 W N
309 B N
310 W L
311 B R
312 B R
313 B L
314 B R
315 B L
316 B R
317 B R
318 W L
319 W L
320 B R
321 B R
322 B R
323 B R
324 B R
325 B L
326 B R
327 W N
328 B L
329 W L
330 B R
331 W L
332 W L
333 B L
334 B L
335 B R
336 W L
337 W L
338 B R
339 B L
340 B R
341 W L
342 B R
343 B R
344 W R
345 W R
346 B R
347 W R
348 W R
349 W L
350 B L
351 W L
352 B R
353 W L
354 B L
355 W R
356 W R
357 B L
358 B R
359 W R
360 B R
361 W L
362 B L
363 B L
364 B R
365 W L
366 B L
367 B R
368 W R
369 B R
370 B L
371 B L
372 W R
373 W L
374 W R
375 B L
376 W L
377 B L
378 B L
379 W L
380 B R
381 B N
382 W N
383 B N
384 B L
385 W L
386 W R
387 B R
388 W L
389 B L
390 B L
391 W L
392 B R
393 W L
394 W L
395 B L
396 W R
397 W L
398 B R
399 B R
400 B R
c. If we restrict our attention to workers who like to drink beer, what is the probability that a randomly selected blue-collar worker prefers to drink light beer?

Solution Summary

The required probabilities are calculated.

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