Given :  In a survey, of 410 salesperson & 350 construction workers, it's found that 164 of salesperson & 196 of construction workers are overweight. a person is selected at random from group

To find :  1. This person is over weight 2. This person is salesperson, given that the person is over weight. 3. This person is over weight, given that the person is a salesperson. 4. This person is a construction worker, given that the person is not over weight. 5. This person is not over weight, given that the person is a construction worker.

Solution:

Sales person  = 410

Overweight sales person = 164

Not Overweight sales person = 410 - 164  = 246

Construction worker 350

Overweight construction worker 196

Not overweight construction worker = 350 -196 = 154

Total Person = 410 + 350 = 760

Total Overweight = 164 + 196 = 360

Total Not overweight = 246 + 154  = 400

Probability Person is over weight   =  Total overweight / total person =  360/760  

=  9/19

Probability person is salesperson, given that the person is over weight. =  Overweight sales person /  total overweight  =  164/360  

= 41/90

Probability person is over weight, given that the person is a salesperson

= Overweight Sales person / total Sales person

=  164 / 410

= 82/205

Probability  person is a construction worker, given that the person is not over weight.   =  not overweight construction worker / total not overweight

= 196/400

= 49/100

Probability  person is not over weight, given that the person is a construction worker = not overweight construction worker / Construction worker

= 196/350

= 14/25

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