PR O BABIL IT IES FR OM TWO WAY TABLES

543.359195)( 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?

PR O BABIL IT IES FR OM 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?

PR O BABIL IT IES FR OM 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?

PR O BABIL IT IES FR OM 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

?

PR O BABIL IT IES FR OM 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?

PR O BABIL IT IES FR OM 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

PR O BABIL IT IES FR OM 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  50 950 1000

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

HappyUnhappy

Totals460290

1000

330170

500

540500210