probabilities from two way tables stustafftotal american107105212 european331245 asian5547102...
TRANSCRIPT
PROBABILIT IES FROM TWO WAY TABLES
543.359
195)( StudentP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
12) What is the probability that the driver is a student?
PROBABILIT IES FROM TWO WAY TABLES
35945
)( EuropeanP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
13) What is the probability that the driver drives a European car?
PROBABILIT IES FROM TWO WAY TABLES
35947
)( AsianandStaffP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
14) What is the probability that the driver is staff and drives an Asian car?
PROBABILIT IES FROM TWO WAY TABLES
359102212
)(
AsianorAmericanP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
15) What is the probability that the driver drives an American or Asian car?
Disjoint?
PROBABILIT IES FROM TWO WAY TABLES
35947102164
)(
AsianorStaffP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
16) What is the probability that the driver is staff or drives an Asian car?
Disjoint?
PROBABILIT IES FROM TWO WAY TABLES
195107
)|( StudentAmericanP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
17) If the driver is a student, what is the probability that they drive an American car?
Condition
PROBABILIT IES FROM TWO WAY TABLES
4533
)|( EuropeanStudentP
Stu Staff TotalAmerican 107 105 212European 33 12 45Asian 55 47 102Total 195 164 359
18) What is the probability that the driver is a student if the driver drives a European car?
Condition
Example 19:Management has determined that customers return 12% of the items assembled by inexperienced employees, whereas only 3% of the items assembled by experienced employees are returned. Due to turnover and absenteeism at an assembly plant, inexperienced employees assemble 20% of the items. Construct a tree diagram or a chart for this data.
Returned Not returned
Total
Experienced 2.4 77.6 80
Inexperienced 2.4 17.6 20
Total 4.8 95.2 100
Example 19:Management has determined that customers return 12% of the items assembled by inexperienced employees, whereas only 3% of the items assembled by experienced employees are returned. Due to turnover and absenteeism at an assembly plant, inexperienced employees assemble 20% of the items. Construct a tree diagram or a chart for this data.
What is the probability that an item is returned?
If an item is returned, what is the probability that an inexperienced employee assembled it?
P(returned) = 4.8/100 = 0.048
P(inexperienced|returned) = 2.4/4.8 = 0.5
Only 5% of male high school basketball, baseball, and football players go on to play at the college level. Of these, only 1.7% enters major league professional sports. Of the athletes that do not play college sports, only 0.1% enters major league professional sports.
What is the probability that a high school athlete will play professional sports?
What is the probability that a high school athlete does not play college sports if he plays professional sports?
Play college Not play college 1.7% of 50
total
Play pro
.85 .95 1.8
Not play pro 49.15 949.05 998.2
Total
50 9501000
Make up a population size!
1.7% of 50
5% of 1000
P(play pro) = P(play college & Play pro) or P(not play college & play pro) = .05(.017) + (.95)(.001) = .0018
P(not play college | plays pro) = P(not play college & play pro) / P(play pro) = .95/1.8 = .5278
People leaving a football match were asked if they supported Manchester United or Newcastle.They were also asked if they were happy. The probability supporting Manchester United is .46. The probability that they support Manchester United and are unhappy is .29. The probability that they support Newcastle and are happy is .33.
Manchester
United
Newcastle
Totals
Happy
Unhappy
Totals460
290
1000
330170
500
540
500210